Target detection by marine radar

Target Detection by Marine Radar John N. Briggs The Institution of Electrical Engineers Published by: The Institution...

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Target Detection by Marine Radar John N. Briggs

The Institution of Electrical Engineers

Published by: The Institution of Electrical Engineers, London, United Kingdom © 2004: The Institution of Electrical Engineers This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Inquiries concerning reproduction outside those terms should be sent to the publishers at the undermentioned address: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts., SGI 2AY, United Kingdom While the author and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the author nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data Briggs, John Target detection by marine radar. - (IEE radar series ; 16) 1 .Tracking radar 2.Radar in navigation !.Title !!.Institution of Electrical Engineers 623.8#933 ISBN 0 86341 359 5

Typeset in India by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in the UK by MPG Books Limited, Bodmin, Cornwall

Foreword

The opportunity arose, with the end of hostilities in 1945, to make available to Merchant Shipping the new technology of radar, which had developed so rapidly in the secrecy of war. In the United Kingdom, the Government made a design available to manufacturers and this was followed by Performance Specifications for Radar for Merchant Ships in 1946. This specification and its later revisions were prepared by the Ministry of Transport in consultation with representatives of shipowners, lighthouse and harbour authorities, marine manufacturers, the General Post Office and the Admiralty. The GPO at the time were responsible for the use of radio frequencies and the Admiralty contributed the technical expertise with a new Transport Experimental group at ASE (Admiralty Signals Establishment) in Eastney which subsequently developed into the Civil Marine Division of ASWE (Admiralty Surface Weapons Establishment). Together with these Performance Specifications a system of type testing of designs was put in place to certify their compliance. Radar on Merchant Ships was initially installed for commercial purposes. The early customers were ferries, which could then maintain better schedules in fog, and large fishing vessels. Radar was treated with great suspicion by the mariners of the day and was usually the preserve of the master, who locked it so that it could only be used when he was on the bridge. Ports also started using radar for the commercial purposes of berthing ships in fog; one example is the Port of Liverpool, in 1948. With improving technology and ease of use, the Merchant Ship radar became more accepted but it was some time before the use of radar for safety purposes was recognised. In fact the melancholy situation in the 1950s was that the introduction of radar had not resulted in any reduction of the number of serious collisions at sea. The collision between the passenger ships Andrea Doria and Stockholm off Nantucket in 1956 is a well recorded example of the misinterpretation of radar information in a passing situation in fog. Accordingly the International Conference on The Safety of Life at Sea in 1960 revised the International Regulations for Preventing Collisions at Sea by adding rules to take account of the use of radar and recommendations on the use of radar information as an aid to avoiding collisions at sea. Today radar with plotting is accepted by mariners as the primary tool to assist in collision avoidance. The International Conference on Safety of Life at Sea in 1974 adopted provisions making radar a mandatory carriage requirement for Merchant

Ships in a phased programme starting in 1980 and finally completed in 2002. All Merchant Ships over 300 gross tonnage now carry a radar and many carry two. Many small craft also carry radar voluntarily as manufacturers have produced cost effective designs for their needs. The Maritime and Coastguard Agency is the direct successor of the Marine Safety Division of the 1946 Ministry of Transport and the consultation processes used then in agreeing radar specifications are still used today through its Safety of Navigation Committee. The task is somewhat more complicated today as specifications are seldom written for national needs but are designed to be internationally agreed so that standards can be maintained all over the world. The ensuing type approval process has also led to international agreement with one approval often being acceptable to Administrations world-wide. No standard setting of the regulatory bodies of the world would be successful, however, if the basic physics of the radar and the resulting technology constraints were not fully understood by those responsible for the drafting. The author of this book is to be congratulated in his descriptions of the physical processes at work and the methods by which the technology can be used in the specialised world of civil marine radar. Kim Fisher FRIN FIEE MCA Chairman UKSON

Preface

Radar is a legal necessity for the safe navigation of merchant ships, is voluntarily carried by many leisure craft, within vessel traffic services (VTS) is indispensable to the operation of major ports and harbours, and has several important other maritime applications. This book tells how these civil surveillance radars detect their targets. Brief historical outlines help explain the way modern practice developed from the first faltering steps of the 1930s. We describe and illustrate today's radars, as well as passive and active beacon targets. But natural features such as coastlines and - vital for collision avoidance - vessels of all shapes and sizes are not specifically designed to reflect radar transmissions. Radar operation however relies on their ability to return echoes. This ability is therefore examined in detail from both practical and theoretical standpoints. Our reason for adding to the many existing radar treatises is, for the first time, to concentrate solely on the civil marine scene, unadulterated by consideration of aircraft flying at 40000 ft, stand-off jammers, Doppler effects and the host of other factors, civil and military, which do not concern civil marine operations. Radar design is constrained by the laws of man and of physics, so we explain the framework lying behind the numerous international regulations governing marine radar and highlight the fundamental technical constraints. Detection is an engineering problem founded on scientific and statistical principles, so we have to include more mathematics than we might wish, but which can be skipped on first reading. Without excluding anything of practical significance, we have simplified our account as much as possible, helping the many users, managers and regulators whose backgrounds lie elsewhere, even perhaps outside the marine industry. We include full technical analysis of the many factors in play within the radars and within targets, the great and sometimes under-estimated parts taken by the weather and the environment, and not least, the ability of operators to set the controls to influence performance for good or ill. Our analysis shows why, when and whether radar will pick up targets as diverse as yachts, low-lying coasts or super-tankers. Numerous graphical and other diagrams and worked examples help the reader to grasp the principles underlying radar operation and to quantify the practical importance of the many factors in play. The analysis culminates in full instructions for use of a set of spreadsheets, available on the IEE website (www.iee.org), which give detection

ranges, probability of detection and many other performance parameters for the user's own equipment, illustrated by a set of case studies. The accuracy with which targets are positioned on the radar screen and with which their progress is tracked and predicted depends upon how definitely they have been detected, so we devote a chapter to the general question of accuracy, which underlies the ability of plotting aids such as ARPA to predict closest point of approach and give other warnings vital to the navigator. Not being master mariners, we leave interpretation of the displayed traces to the specialist navigation textbooks. In the final chapter, Chris Baker looks at some of the ways in which marine radar may develop to meet the challenges of the next two decades. We have striven to be comprehensive, minimising the need to hunt up references elsewhere. Copious cross-references, a logical layout, the glossary and the index should quickly guide the busy reader to specific items. Although we authors take full responsibility for the errors and omissions that surely remain, this book would have been impossible without the help, advice and encouragement of many experts. J.N.B. would like to thank several old GEC-Marconi colleagues whose friendship often goes back too many years to admit. They include John Ashley, Niall Davies, Steve Holland, George Hurd who made extensive comments on an early draft, Bob James, David Ogleby who identified the need for such a book when scheming VTS systems, Richard Parsons, Janet and Peter Sykes, and Dudley Taylor whose computer expertise was vital at times. Several friends with senior engineering management experience elsewhere in the marine radar industry freely gave valuable help, including among others David Hannah, Richard Trim and Professor Phil Williams. J.N.B. is particularly in debt to Phil for valuable comments on the whole draft text and for permission to quote freely from his privately published CD work 'Civil Marine Radar' with its wealth of technical detail and historical aspects describing the evolution of Decca radars. In the early days Professor John Kemp, then Editor of the Journal of Navigation and Julian Parker, then Secretary of the Nautical Institute gave valuable encouragement to persevere with what seemed a daunting endeavour. The Royal Institute of Navigation generously supplied a scarce copy of The Uses of Radar at Sea. Jonathan Ansell of Easat Antennas freely gave much background information on modern VTS and scanner developments, while Peter Munro of Munro Engineering kindly read and commented on Chapter 8. Officials have been equally helpful. Martin Hart and his colleagues at the Maritime and Coastguard Agency checked and corrected the regulatory sections of Chapter 1 and looked up a number of technical points. J.N.B. also benefited from extensive discussions with Roy Lee on regulatory aspects. Dr J. M. Williams took much trouble to explain the fundamentals of ships' radar reflectivity, which Chapter 10 attempts to summarise. Bill Paterson, then Director of Engineering, Northern Lighthouse Board, facilitated the atmospheric refraction experiments described in Chapter 5. Dr Nick Ward, Principal Development Engineer, Trinity House Lighthouse Service, kindly dug out a number of IALA papers and supplied illustrations. A number of leading manufacturers and other organisations also kindly contributed illustrations, as acknowledged in the text. We do not however endorse particular

suppliers' products - all the leading manufacturers offer highly developed equipment capable of excellent performance. Other illustrations are from the authors' collections. J.N.B. would like to thank Sarah Kramer, Commissioning Editor at the IEE, and the IEE team for their forbearance, also Professor Hugh Griffiths, Radar Series Editor. His predecessor, Professor Ramsay Shearman, gave much guidance and prevailed on Professor Baker to contribute to the book. Finally, and most important of all, J.N.B. must record his thanks to his longsuffering wife Betty for putting up with the disruption of the supposed leisure of retirement with 'yet more work'. Chris Baker is especially indebted to Professor Hugh Griffiths (University College London), Dr Andy Stove (THALES Sensors), Dr Steve Harmari and Mr Graham Binns (QinetiQ) and Professor Ramsay Shearman for their invaluable advice and numerous corrections to Chapter 16. In particular C. J.B. wishes to thank J.N.B. for the invitation to write the chapter and for having the patience to integrate it with the earlier chapters.

Contents

Foreword ............................................................................. xxv Preface ................................................................................ xxvii 1.

Introduction .................................................................

1

1.1

Purpose and Scope .......................................................

1

1.1.1

Purpose .......................................................

1

1.1.2

Scope ..........................................................

3

Radar Users and Uses ..................................................

4

1.2.1

Merchant Ships ............................................

4

1.2.2

Leisure Craft ................................................

5

1.2.3

Fishing Vessels and Small Commercial Vessels ........................................................

5

1.2.4

High Speed Craft .........................................

5

1.2.5

Vessel Traffic Services ................................

5

1.2.6

Military Applications .....................................

6

The Past and Future ......................................................

7

1.3.1

The History of Marine Radar ........................

7

1.3.2

Secondary Radars .......................................

10

1.3.3

VTS .............................................................

12

1.3.4

The Current Generation of Radars ...............

13

1.3.5

Future Possibilities .......................................

14

The Regulators ..............................................................

15

1.4.1

15

1.2

1.3

1.4

Overview ......................................................

This page has been reformatted by Knovel to provide easier navigation.

v

vi

Contents 1.4.2

UNCLOS ......................................................

15

1.4.3

IMO ..............................................................

15

1.4.4

National Consultations .................................

16

1.4.5

SOLAS and the Colregs ...............................

17

1.4.6

IALA .............................................................

17

1.4.7

Enforcement ................................................

18

1.4.8

ISO ..............................................................

18

1.4.9

IEC ..............................................................

18

1.4.10 ITU ...............................................................

19

1.4.11 National Regulations ....................................

19

1.4.12 National and Supra-national Groups; the European Community ............................

19

1.4.13 The Courts ...................................................

20

The Regulations .............................................................

21

1.5.1

Radar for Ships within SOLAS .....................

21

1.5.2

Radar for Craft Outside SOLAS ...................

23

Theory and Calculations ................................................

23

1.6.1

Sources .......................................................

23

1.6.2

Mathematics and Units ................................

24

1.6.3

Basis of Performance Calculations ..............

26

1.6.4

Spreadsheet Calculation ..............................

26

1.6.5

Approximate Methods ..................................

26

1.7

The Layout of This Book ...............................................

27

1.8

References ....................................................................

28

The System and the Transmitter ...............................

31

2.1

The Operator and the System .......................................

31

2.1.1

Scope of Chapter .........................................

31

2.1.2

Operators Afloat ...........................................

31

2.1.3

Integrated Bridge Systems ...........................

35

2.1.4

Operators Ashore ........................................

35

1.5

1.6

2.


Contents

vii

2.1.5

Basic Radar Operation .................................

37

2.1.6

Target Detectability ......................................

39

2.1.7

Radar Construction ......................................

41

2.1.8

Decibels .......................................................

42

Components of the Radar .............................................

44

2.2.1

Transmission ...............................................

44

2.2.2

Reception ....................................................

47

2.2.3

Non-coherent System ..................................

48

2.2.4

Coherent-on-receive System .......................

48

2.2.5

Fully Coherent System .................................

50

2.2.6

Ambiguity; Image Frequency, prf Constraints ..................................................

50

Typical Station Configuration .......................

51

Transmitter .....................................................................

52

2.3.1

Overview ......................................................

52

2.3.2

Magnetron Power Source ............................

53

2.3.3

Modulator .....................................................

54

2.3.4

Influence of Transmitter on System ..............

55

2.3.5

Spectrum Problems .....................................

55

Transmitted Frequency .................................................

57

2.4.1

Frequency and Wavelength .........................

57

2.4.2

Choice of Band ............................................

59

2.5

Choice of Other Parameters ..........................................

59

2.6

Feeder ............................................................................

60

2.6.1

Waveguide ...................................................

60

2.6.2

Mismatch .....................................................

64

2.6.3

Feeder Losses .............................................

66

2.6.4

Ringing ........................................................

67

Scanner, Qualitative Description ...................................

67

2.7.1

Plane and Circularly Polarised Rays ............

67

2.7.2

Directional Radiation ....................................

69

2.2

2.2.7 2.3

2.4

2.7


viii

Contents

2.8

2.7.3

Beam Characteristics ...................................

71

2.7.4

Rotation .......................................................

72

2.7.5

Size and Beamwidth ....................................

72

2.7.6

Marine Radar Scanners ...............................

72

2.7.7

Radiation Patterns .......................................

74

2.7.8

Recent Developments ..................................

77

2.7.9

Obstructions ................................................

78

2.7.10 Sidelobes .....................................................

78

2.7.11 VTS Reflector Scanners ..............................

79

2.7.12 Elevation Performance; Inverse Cosecant Squared Reflectors ......................

82

2.7.13 Polarisation ..................................................

83

2.7.14 Surface Tolerance Loss ...............................

84

2.7.15 Beamshape and Scanning Losses ...............

85

2.7.16 Summary of Scanner Losses .......................

86

2.7.17 Testing Antennas .........................................

86

Quantitative Scanner Analysis ......................................

88

2.8.1

Elevation Performance, Marine and VTS Slotted Arrays ......................................

88

Inverse Cosecant Squared VTS Scanners .....................................................

90

Azimuth Radiation Pattern ...........................

92

References ....................................................................

93

Radar Receiver ............................................................

95

3.1

Scanner – Receiving .....................................................

95

3.2

Receiver Input ................................................................

96

3.2.1

Rotating Joint or Sliprings ............................

96

3.2.2

Receiver Protection .....................................

96

3.2.3

Duplexer ......................................................

97

Receiver and Filter ........................................................

98

3.3.1

98

2.8.2 2.8.3 2.9

3.

3.3

Overview ......................................................


Contents 3.3.2 3.4

3.5

3.6

3.7

3.8

3.9

ix

Receiver Noise ............................................ 100

Superhet Receiver and Mixing ...................................... 104 3.4.1

Superheterodyne Principle ........................... 104

3.4.2

Mixing .......................................................... 104

3.4.3

Local Oscillator ............................................ 106

IF Amplifier, Demodulator and Video Sections ............. 106 3.5.1

IF Section .................................................... 106

3.5.2

Filter ............................................................ 107

3.5.3

Linear and Square-law Demodulators .......... 109

3.5.4

Factors Affecting Detection .......................... 110

3.5.5

Detection Cells ............................................. 111

3.5.6

Effect of Range Scale Selection ................... 111

3.5.7

Video Amplifier ............................................. 112

3.5.8

Fast Time Constant, Differentiator ............... 113

Signal Processing Basics .............................................. 115 3.6.1

The Task ...................................................... 115

3.6.2

PD and PFA for Target Perception ................. 116

3.6.3

Digital Conversion, Detection Cells .............. 117

3.6.4

Logical Process of Target Detection ............ 118

3.6.5

Machine Detection ....................................... 119

3.6.6

Clutter Map .................................................. 120

3.6.7

Detection Decision Process ......................... 121

Additional Features ........................................................ 123 3.7.1

Within Single Radar ..................................... 123

3.7.2

Multiple Sensors, Track Combiners ............. 123

Display Principles .......................................................... 124 3.8.1

Display Format ............................................. 125

3.8.2

Cathode Ray Tube ....................................... 126

3.8.3

Other Display Devices ................................. 127

Raster Scan Display ...................................................... 127


x

Contents 3.10 Cursive Display .............................................................. 130 3.10.1 Raw Radar ................................................... 130 3.10.2 Cursive Display Problems ............................ 132 3.10.3 Detection Performance ................................ 133 3.11 Plots on the Screen ....................................................... 133 3.12 Radars for Special Purposes ......................................... 134 3.12.1 High Speed Craft ......................................... 134 3.12.2 Warships ...................................................... 135 3.13 Calibration ...................................................................... 135 3.14 References .................................................................... 136

4.

Echo Strength in Free Space ..................................... 137 4.1

Introduction .................................................................... 137

4.2

Radiated Power Density ................................................ 138

4.3

Passive Reflector; Radar Cross Section, Radar Range Equation ............................................................. 138 4.3.1

Radar Cross Section .................................... 138

4.3.2

Two-way Free Space Radar Range Equation ...................................................... 139

4.4

Active Target .................................................................. 141

4.5

Range Equations in Practical Form ............................... 141

4.6

4.7

4.5.1

Extensions for Practical Environment ................................................. 141

4.5.2

Full Radar Range Equation, dB ................... 142

4.5.3

Reduced Equations ...................................... 142

Calculations and Graphs ............................................... 143 4.6.1

Fixed Range Example .................................. 143

4.6.2

Graphs ......................................................... 144

4.6.3

Computer Spreadsheet and Charting ....................................................... 148

Limitations of Free Space Formulae ............................. 148


Contents 5.

xi

Environmental Effects on Propagation ..................... 151 5.1

Scope of Chapter ........................................................... 151

5.2

Atmospheric Refraction ................................................. 152 5.2.1

The Problem ................................................ 152

5.2.2

Equivalent Geometries ................................. 154

5.2.3

Calculation of Refraction Factor from Meteorological Parameters .......................... 155

5.2.4

Standard Atmosphere; Four-thirds Earth Approximation .................................... 157

5.2.5

Anaprop ....................................................... 157

5.2.6

Super-refraction; High k; Superstandard Surface Layer ................................ 158

5.2.7

Negative k .................................................... 159

5.2.8

Sub-refraction; Low k; Sub-standard Surface Layer .............................................. 159

5.2.9

Ducts ........................................................... 159

5.2.10 Conditions Causing Anaprop ....................... 160 5.3

Measurement of Refraction Factor ................................ 161

5.4

Ray Geometry; Geometrical Optics .............................. 163

5.5

5.4.1

Introduction .................................................. 163

5.4.2

Importance of k Depends on Range ............. 165

Geometrical Analysis, Curved Earth ............................. 166 5.5.1

Ray Paths .................................................... 166

5.5.2

Range .......................................................... 168

5.5.3

Path Difference of Indirect Ray .................... 170

5.5.4

Useful Angles ............................................... 171

5.5.5

Divergence Factor ....................................... 173

5.5.6

Variation of Geometrical Parameters with Range ................................................... 173

5.5.7

Horizon ........................................................ 175

5.5.8

Multipath Peak and Null Ranges .................. 176


xii

Contents 5.5.9 5.6

5.7

5.8

5.9

Effect on Detection Range ........................... 177

Flat-earth Approximation ............................................... 177 5.6.1

Geometrical Analysis ................................... 177

5.6.2

Approximate Multipath Ranges .................... 178

5.6.3

Tailoring Null Ranges ................................... 179

5.6.4

Vertical Lobe Structure ................................ 179

5.6.5

Dispersion .................................................... 181

The Sea ......................................................................... 181 5.7.1

Capillary and Gravity Waves ........................ 182

5.7.2

Radar Reflection, Capillaries Alone ........................................................... 184

5.7.3

Radar Reflection, Gravity Waves ................. 185

5.7.4

Wave Height ................................................ 186

5.7.5

Sea State ..................................................... 187

Forward Reflection from the Grazing Point ................... 189 5.8.1

Reflection Coefficient Amplitude .................. 189

5.8.2

Reflection Coefficient, ρ0, of Smooth Plane Surface .............................................. 189

5.8.3

Reflection Coefficient Variation .................... 191

5.8.4

Reflection Coefficient, ρs, of Surface Roughness .................................................. 193

5.8.5

Values of ρs .................................................. 196

5.8.6

Values of ρ ................................................... 196

Atmospheric and Precipitation Losses .......................... 196 5.9.1

Causes of Loss ............................................ 196

5.9.2

Rain ............................................................. 198

5.9.3

Snow and Hail .............................................. 200

5.9.4

Fog, Low Cloud and Sandstorms ................. 201

5.9.5

Clear Air Attenuation .................................... 203

5.9.6

Spray ........................................................... 205

5.9.7

Total Atmospheric Attenuation ..................... 205


Contents 5.9.8

xiii

Foliage ......................................................... 205

5.10 References .................................................................... 206

6.

Multipath of Point Targets .......................................... 207 6.1

Introduction .................................................................... 207 6.1.1

The Problem ................................................ 207

6.1.2

Definition of Multipath Factor ....................... 208

6.1.3

Correction for Scanner Elevation Beamwidth ................................................... 208

6.1.4

Chapter Layout ............................................ 208

6.2

Effective Scanner Gain .................................................. 209

6.3

Multipath Regions .......................................................... 209

6.4

6.5

6.6

6.7

6.3.1

Regions ....................................................... 209

6.3.2

Boundaries .................................................. 212

6.3.3

Transition and Diffraction Boundary Ranges ........................................................ 213

Interference Region ....................................................... 215 6.4.1

Value of Multipath Factor ............................. 215

6.4.2

Average Value of Multipath Factor ............... 218

6.4.3

Narrow Pulses ............................................. 219

6.4.4

Diversity ....................................................... 219

Diffraction Region .......................................................... 220 6.5.1

The Nature of Diffraction .............................. 220

6.5.2

Calculation of Diffraction .............................. 220

6.5.3

Change of Multipath Factor with Range .......................................................... 222

6.5.4

Effect of Height ............................................ 223

Transition Region .......................................................... 223 6.6.1

Approach ..................................................... 223

6.6.2

Solution of Multipath Equation ..................... 224

Overall Multipath Factor ................................................ 225 6.7.1

Full Method .................................................. 225


xiv

Contents 6.7.2 6.8

6.9

Flat-earth Approximation .............................. 226

Two-zone Method .......................................................... 227 6.8.1

General Form of Multipath/Range Relationship ................................................. 227

6.8.2

Rate of Change of Multipath Factor at RA, Calm Sea ............................................... 227

6.8.3

Approximation for Multipath Factor in Near Transition Region ................................ 228

6.8.4

Approximate Multipath Factor Near Horizon ........................................................ 230

6.8.5

Very Low Scanner or Target ........................ 231

Sketching Echo Strength ............................................... 231 6.9.1

Use of Sketches ........................................... 231

6.9.2

Scales .......................................................... 232

6.9.3

Sketching Echo, Fair Weather ..................... 232

6.9.4

Sketching Echo, Rough Sea ........................ 234

6.9.5

Really Rough Sketch ................................... 234

6.9.6

Accuracy ...................................................... 235

6.10 References .................................................................... 236

7.

Passive Point Targets ................................................ 237 7.1

7.2

Introduction .................................................................... 237 7.1.1

Structure of RCS Discussions ...................... 237

7.1.2

Applications of Point Passive Reflectors .................................................... 239

7.1.3

Meanings ..................................................... 239

Reflection from Insulators .............................................. 239 7.2.1

Basic Process .............................................. 239

7.2.2

Secondary Reflections ................................. 241

7.2.3

Materials ...................................................... 243

7.2.4

Reflecting Shapes ........................................ 243


Contents 7.3

7.4

xv

Reflection from Conductors ........................................... 245 7.3.1

Principles ..................................................... 245

7.3.2

Target Dimensions Very Many Wavelengths ................................................ 245

Reflection from Basic Metal Shapes ............................. 246 7.4.1

Introduction .................................................. 246

7.4.2

Calculation of RCS; Definitions .................... 247

7.4.3

Sphere ......................................................... 248

7.4.4

Disc and Flat Plate ....................................... 249

7.4.5

Macro- and Micro-geometry; Distorted Plate ............................................................ 252

7.4.6

Dihedral Corner Reflector ............................ 253

7.4.7

Distorted Corner .......................................... 254

7.4.8

Practical Effects of Micro-geometry .............. 255

7.4.9

Edges and Rods .......................................... 255

7.4.10 Circular Polarisation ..................................... 255 7.5

7.6

7.7

Other Geometric Shapes ............................................... 256 7.5.1

Cylinder, Metal Wire ..................................... 256

7.5.2

Circular Cone ............................................... 257

7.5.3

Frequency Effects ........................................ 257

Requirements for Practical Reflectors ........................... 257 7.6.1

Legal Requirements, Specifications ............. 257

7.6.2

Measurement of Point Aids .......................... 259

7.6.3

Commercial Reflectors ................................. 259

7.6.4

Problems with Reflectors ............................. 261

Practical Reflectors ........................................................ 261 7.7.1

Trihedral ...................................................... 261

7.7.2

Octahedral ................................................... 262

7.7.3

Trihedral Clusters ........................................ 265

7.7.4

Luneberg Lens ............................................. 266

7.7.5

Helispherical Reflector ................................. 268


xvi

Contents

7.8

7.9

7.7.6

Lens Reflectors ............................................ 269

7.7.7

Chaff ............................................................ 269

7.7.8

Phased Patch Array Reflectors .................... 269

Miscellaneous Point Targets ......................................... 270 7.8.1

Aircraft ......................................................... 270

7.8.2

Helicopters ................................................... 271

7.8.3

Buoys and Lighthouses ................................ 271

7.8.4

Birds ............................................................ 272

7.8.5

Man ............................................................. 273

7.8.6

Scanners ..................................................... 273

7.8.7

Flotsam ........................................................ 273

Tilting a Point Target Aid ............................................... 273 7.9.1

Introduction .................................................. 273

7.9.2

Radar in Roll Plane ...................................... 274

7.9.3

Radar Normal to Roll Plane ......................... 274

7.10 Combination of Point Targets ........................................ 275 7.10.1 The Problem ................................................ 275 7.10.2 Assumptions and Notation ........................... 275 7.10.3 Resultant Performance of Pair ..................... 276 7.10.4 Examples ..................................................... 278 7.10.5 Response in Other Plane; TPM .................... 280 7.10.6 RCS Fluctuation ........................................... 280 7.10.7 Tilt ................................................................ 281 7.10.8 Practical Performance .................................. 282 7.11 References .................................................................... 283

8.

Active Targets ............................................................. 285 8.1

Introduction .................................................................... 285 8.1.1

Passive and Active Reflectors ...................... 285

8.1.2

Historical ...................................................... 286

8.1.3

Features of Active Devices .......................... 287


Contents

8.2

xvii

8.1.4

Overload ...................................................... 289

8.1.5

Interference ................................................. 290

8.1.6

Response Law; Effective RCS ..................... 290

8.1.7

Specifications and Legal Requirements .............................................. 290

8.1.8

Structure of Chapter ..................................... 291

8.1.9

Polarisation Compatibility ............................. 291

Description of Conventional Racons ............................. 293 8.2.1

Function ....................................................... 293

8.2.2

Swept Frequency and Agile Types ............... 294

8.2.3

Traffic Capacity ............................................ 295

8.2.4

Interference ................................................. 296

8.2.5

Detection at the Racon ................................ 296

8.2.6

Swept Frequency Racon Response ............. 296

8.2.7

Frequency Agile Racon Response ............... 298

8.2.8

Functional Description ................................. 301

8.2.9

Sidelobe Suppression .................................. 301

8.2.10 Target Pattern Map ...................................... 302 8.2.11 Low Pass Filter ............................................ 302 8.2.12 Idling ............................................................ 304 8.2.13 Self Test ...................................................... 304 8.3

8.4

Racon Problems ............................................................ 304 8.3.1

Effect of Swept Gain .................................... 304

8.3.2

Tuning Errors ............................................... 304

8.3.3

Chirp ............................................................ 305

Racon Performance Analysis ........................................ 306 8.4.1

Notation ....................................................... 306

8.4.2

Interrogation Received at Racon .................. 307

8.4.3

Probability of Detection ................................ 308

8.4.4

Response on Axis ........................................ 308

8.4.5

Equivalent RCS ........................................... 309


xviii

Contents

8.5

8.6

8.7

8.8

8.9

8.4.6

Sidelobes ..................................................... 310

8.4.7

Example ....................................................... 310

8.4.8

Balance between Legs ................................. 311

8.4.9

Interaction .................................................... 315

User-selectable Racons ................................................ 315 8.5.1

The Problem ................................................ 315

8.5.2

Fixed Frequency and Fixed Offset Frequency Racons ....................................... 316

8.5.3

ITOFAR ....................................................... 316

8.5.4

USIFAR ....................................................... 317

Miscellaneous in-band Racons ..................................... 317 8.6.1

Step-sweep Racons ..................................... 317

8.6.2

Fast-sweep Racons ..................................... 318

8.6.3

High Power Racons ..................................... 318

Cross-band Racons and Transponders ........................ 318 8.7.1

Radar/Radio Systems .................................. 319

8.7.2

Radar Automatic Identification System ........ 319

SARTs ............................................................................ 320 8.8.1

Purpose ....................................................... 320

8.8.2

Sweep Regime ............................................ 321

8.8.3

Display on Radar ......................................... 321

8.8.4

Performance Equations – Sweep Loss ........ 322

Ramarks ......................................................................... 324

8.10 Radar Target Enhancers ............................................... 324 8.10.1 Principle ....................................................... 324 8.10.2 Basic Description ......................................... 326 8.10.3 Ancillary Facilities ........................................ 328 8.10.4 Specification ................................................ 328 8.10.5 Radar Cross Section .................................... 328 8.10.6 RTE Response on Axis ................................ 329 8.10.7 Unsaturated RCS ......................................... 331


Contents

xix

8.10.8 Saturated RCS, Saturation Range ............... 331 8.10.9 Sidelobes ..................................................... 332 8.10.10 Target Pattern Map ...................................... 333 8.10.11 Noise Power Output ..................................... 333 8.10.12 Example of RTE Noise ................................. 334 8.10.13 Example of RTE Performance ...................... 335 8.10.14 Interaction .................................................... 337 8.10.15 Problems and Opportunities ......................... 337 8.11 Miscellaneous Devices .................................................. 337 8.11.1 Scanner RCS ............................................... 337 8.11.2 Modulated Reflectors ................................... 338 8.12 Target Tilted in Radar/Target Plane .............................. 338 8.12.1 General ........................................................ 338 8.12.2 Racons and SARTs ..................................... 339 8.12.3 Unsaturated RTEs ....................................... 340 8.12.4 Saturated RTEs ........................................... 340 8.13 Target Tilted Normal to Radar-target Plane .................. 341 8.13.1 General ........................................................ 341 8.13.2 Horizontally Polarised Racons, SARTs and Saturated RTEs; Linearly Polarised Scanner ....................................................... 341 8.13.3 Circularly Polarised 3 GHz Band Racons ........................................................ 341 8.13.4 Unsaturated RTEs, Slant Polarised Antennas, Linearly Polarised Scanner ......... 342 8.13.5 Saturated RTEs, Slant Polarisation, Linearly Polarised Scanner .......................... 343 8.13.6 Slant Polarised RTEs, Circularly Polarised Scanner ....................................... 343 8.13.7 Unsaturated RTE without Slant Polarisation .................................................. 343 8.14 Target Tilted Oblique to Radar-target Plane ................. 343 This page has been reformatted by Knovel to provide easier navigation.

xx

Contents 8.15 RTE Plus Passive Point Target in Free Space ............. 344 8.15.1 Introduction .................................................. 344 8.15.2 RTE Below Reflector .................................... 344 8.15.3 Passive Reflector Surrounding RTE ............. 346 8.15.4 Delayed RTE ............................................... 346 8.15.5 Practical Conditions, RTE/Reflector Pair .............................................................. 347 8.15.6 Practical Conditions, Racons, SARTs and Ramarks ............................................... 347 8.16

9.

References .................................................. 348

Multipath Factor of Extended Targets ...................... 349 9.1

9.2

9.3

9.4

Introduction .................................................................... 349 9.1.1

The Problem ................................................ 349

9.1.2

Target Echo ................................................. 350

Multipath of Extended Target, Summation Method ........................................................................... 351 9.2.1

Summation of Element Echoes .................... 351

9.2.2

Uniform RCS Distribution; Critical Range .......................................................... 351

9.2.3

Multipath Factor ........................................... 353

Diffraction and Transition Regions ................................ 354 9.3.1

Echo Variation with Element Height ............. 354

9.3.2

Integration, Uniform Target; Height Factor .......................................................... 354

9.3.3

Non-uniform Target ...................................... 355

9.3.4

Choice of Target Height Factor .................... 356

Interference Region ....................................................... 357 9.4.1

Ray Geometry, Cylindrical Target ................ 357

9.4.2

Element Multipath Factor, Flat Earth ............ 357

9.4.3

Target Multipath Factor ................................ 358

9.4.4

Curved Earth ................................................ 360


Contents 9.4.5 9.5

9.6

xxi

Multipath Factor Up to Critical Range .......... 360

Approximate Multipath Factor into Transition Region ............................................................................ 361 9.5.1

Critical Range .............................................. 361

9.5.2

Moderate Sea Condition .............................. 362

9.5.3

High Scanner or Target ................................ 363

Complete Multipath Expression .................................... 364 9.6.1

Multipath Factor ........................................... 364

9.6.2

Variation of Echo with Range ....................... 364

9.6.3

Non-uniform Targets .................................... 365

9.6.4

Sketching Echo Strength ............................. 367

10. Extended Target Reflections; Ships and Coasts .......................................................................... 369 10.1 The Problem .................................................................. 369 10.1.1 Target Parameters Affecting Detection ........ 369 10.1.2 Difficulty of Finding RCS .............................. 370 10.1.3 Factors Affecting RCS Seen by Interrogator .................................................. 370 10.1.4 Estimation of Effective Height ...................... 371 10.1.5 Our Approach .............................................. 371 10.2 Ship Size ........................................................................ 372 10.3 Experimental Determination of RCS and Effective Height ............................................................................. 375 10.3.1 Military Methods ........................................... 375 10.3.2 Radar Measurement of Typical Ship RCS ............................................................. 375 10.3.3 Alternative Measurement Strategies ............ 376 10.3.4 RCS of Specific Vessel ................................ 377 10.3.5 Effective Target Height ................................ 377 10.4 Reported RCS Values ................................................... 379 10.4.1 Limitations ................................................... 379 This page has been reformatted by Knovel to provide easier navigation.

xxii

Contents 10.4.2 Williams et al. .............................................. 379 10.4.3 IALA VTS Manual ........................................ 382 10.4.4 Skolnik ......................................................... 382 10.4.5 Warships ...................................................... 383 10.4.6 A Rule of Thumb .......................................... 383 10.4.7 Radar Technology Encyclopedia .................. 383 10.4.8 Angle of Depression ..................................... 384 10.4.9 Suggested Formula for Merchant Ships ........................................................... 385 10.5 Theoretical Basis for RCS ............................................. 385 10.5.1 Approach ..................................................... 385 10.5.2 Tonnage and Linear Dimensions ................. 387 10.5.3 Micro-geometric Approach; Baseline RCS ............................................................. 387 10.5.4 TPM Smoothness ........................................ 388 10.5.5 RCS/Tonnage by Micro-geometry ................ 389 10.5.6 RCS/Tonnage by Macro-geometry ............... 389 10.5.7 Reconciliation with Reported Results ........... 389 10.6 Features Contributing to Ships’ RCS ............................ 390 10.6.1 Long-range Detectability .............................. 390 10.6.2 Mega-geometry Factors ............................... 391 10.6.3 Macro-geometry Factors .............................. 391 10.6.4 Micro-geometry Factors ............................... 392 10.6.5 Stealthed Vessels ........................................ 392 10.7 Detection Cell Overflow ................................................. 393 10.7.1 Azimuth Overflow ......................................... 393 10.7.2 Range Overflow ........................................... 394 10.7.3 Glint ............................................................. 395 10.7.4 Straddling .................................................... 395 10.8 The RCS to Use for Ships ............................................. 395


Contents

xxiii

10.9 RCS of Small Craft ........................................................ 396 10.9.1 The Problem ................................................ 396 10.9.2 Reflecting Elements ..................................... 397 10.9.3 Displaced Water .......................................... 397 10.10 Fast Craft ....................................................................... 398 10.10.1 High Speed Craft ......................................... 398 10.10.2 Large Motor Yachts ...................................... 399 10.10.3 Wing in Ground (WIG) Craft (Ekranoplanes) ............................................ 399 10.11 Lobe Spacing, Yaw and Roll ......................................... 400 10.12 Land and Shoreside Features ....................................... 401 10.12.1 Introduction .................................................. 401 10.12.2 Coastline and Rivers .................................... 401 10.12.3 Shoals .......................................................... 404 10.12.4 Bridges ........................................................ 404 10.12.5 Overhead Obstructions ................................ 406 10.12.6 False Echoes ............................................... 406 10.12.7 Fluctuation Characteristics ........................... 406 10.13 Ice .................................................................................. 409 10.13.1 Introduction .................................................. 409 10.13.2 Ice Formed in the Water .............................. 410 10.13.3 Bergs and Growlers ..................................... 410 10.13.4 Pack and Fast Ice ........................................ 411 10.13.5 Icebergs Calved from Glaciers ..................... 411 10.13.6 Optimum Radar Bands ................................ 412 10.14 Echo Strength from Extended Targets; Sketches ........................................................................ 412 10.15 References .................................................................... 414

11. Noise, Clutter and Interference .................................. 415 11.1 The Importance of Noise and Clutter to Detection of Targets ....................................................................... 415 This page has been reformatted by Knovel to provide easier navigation.

xxiv

Contents 11.2 Mean Noise .................................................................... 416 11.2.1 Noise Power ................................................ 416 11.2.2 Receiver Input Stage Noise Contribution ................................................. 417 11.2.3 Noise Factor ................................................ 418 11.2.4 Noise Temperature ...................................... 419 11.2.5 Bandwidth .................................................... 419 11.2.6 Environmental Noise Sources ...................... 420 11.2.7 Atmosphere and Line Attenuation Noise ........................................................... 420 11.2.8 System Noise ............................................... 421 11.3 Noise Fluctuation ........................................................... 422 11.3.1 Prediction of Random Events ....................... 422 11.3.2 Individual Noise Contributors Do Not Cancel ......................................................... 422 11.3.3 Amplitude Distribution of Noise .................... 422 11.3.4 Noise Bandwidth .......................................... 422 11.3.5 Amplification ................................................ 423 11.3.6 Event Rate ................................................... 423 11.3.7 Amplitude and Power Conventions .............. 423 11.3.8 Distribution and Probability Density, Unmodulated White Noise ........................... 424 11.3.9 Effect of Atmospheric and Feeder Noise on Signals .......................................... 427 11.4 Mean Precipitation Clutter ............................................. 428 11.4.1 Clutter Mechanism ....................................... 428 11.4.2 Mean Reflectivity ......................................... 428 11.4.3 Polarisation .................................................. 430 11.4.4 Mean Received Clutter Power ..................... 431 11.5 Precipitation Clutter Fluctuation .................................... 433 11.6 Mean Sea Clutter ........................................................... 433 11.6.1 Reflection Mechanism .................................. 433 This page has been reformatted by Knovel to provide easier navigation.

Contents

xxv

11.6.2 Clutter per Unit Area, σS0 ............................. 435 11.6.3 Wave Height Relation to Wind Speed .......... 438 11.6.4 Sea Clutter Mean Power .............................. 438 11.6.5 Effect of Scanner Height .............................. 440 11.6.6 Abnormal Waves ......................................... 441 11.7 Sea Clutter Fluctuation .................................................. 441 11.7.1 Sea Clutter, Low Sea State .......................... 441 11.7.2 Sea Clutter, High Sea State ......................... 441 11.7.3 Log-normal Distribution ................................ 443 11.7.4 Weibull Distribution ...................................... 443 11.8 Short-range Ringing Clutter ........................................... 446 11.8.1 Feeder Ringing ............................................ 446 11.8.2 Example ....................................................... 448 11.8.3 Ghost Axial Echoes ...................................... 449 11.8.4 Receiver Oscillation ..................................... 449 11.9 Man-made Interference ................................................. 449 11.9.1 Other Radars ............................................... 449 11.9.2 Own Ship ..................................................... 451 11.10 References .................................................................... 451

12. Detection ..................................................................... 453 12.1 Outline ............................................................................ 453 12.1.1 What We Mean by Detection ....................... 453 12.1.2 Echo Fluctuations ........................................ 454 12.1.3 Noise and Clutter Fluctuations ..................... 454 12.1.4 Detection in Random Noise or Clutter .......... 455 12.1.5 Assumptions ................................................ 456 12.1.6 The Detection Problem ................................ 457 12.1.7 Rigour .......................................................... 459 12.1.8 Effect of Receiver Type ................................ 459 12.1.9 Chapter Layout ............................................ 459


xxvi

Contents 12.2 Direct Detection of Single Pulse in Noise ..................... 460 12.2.1 Detection Threshold, Unmodulated Noise ........................................................... 460 12.2.2 Detection of Sinusoidal Signal ..................... 462 12.2.3 Variation of PD with SNR .............................. 463 12.3 Envelope Detection of Echo Pulse in Noise .................. 466 12.3.1 Detection in Non-coherent Receiver ...................................................... 466 12.3.2 Equivalent Envelope Detector ...................... 469 12.3.3 Noise Distribution ......................................... 469 12.3.4 Noisy Signal Distribution .............................. 471 12.3.5 Approximations for PD Calculation ................................................... 472 12.3.6 Accuracy ...................................................... 476 12.4 Single Pulse Detection in Clutter ................................... 476 12.4.1 Noise and Precipitation Clutter ..................... 476 12.4.2 Clutter with Weibull Distribution ................... 476 12.4.3 Equivalent Sea, Land and Ice Clutter .......................................................... 477 12.5 Target Fluctuation .......................................................... 480 12.5.1 The Problem ................................................ 480 12.5.2 Swerling Fluctuation Cases .......................... 481 12.5.3 Case 0 (Case 5) Non-fluctuating Target .......................................................... 482 12.5.4 Fluctuating Targets ...................................... 484 12.5.5 Swerling Case 1 ........................................... 485 12.5.6 Swerling Case 2 ........................................... 487 12.5.7 Swerling Case 3a ......................................... 488 12.5.8 Comparison of Fluctuation Cases ................ 489 12.6 Multiple Observations .................................................... 491 12.6.1 Addition of Returns ...................................... 491


Contents

xxvii

12.6.2 Coherent and Non-coherent Integration .................................................... 493 12.6.3 Integration Gain or Loss ............................... 493 12.6.4 Swerling Case 2 Targets .............................. 496 12.6.5 M Out of N Integrators ................................. 498 12.6.6 Performance Margin .................................... 498 12.6.7 Cursive Displays .......................................... 498 12.6.8 Analog Integration ........................................ 499 12.6.9 Mitigation of Losses in Small Scanners and Wide Bandwidth .................................... 499 12.6.10 Logarithmic Receiver Loss ........................... 500 12.6.11 Detection at Short Range with Ringing ........ 500 12.7 Setting the Threshold .................................................... 500 12.7.1 Interchangeability of Receiver Gain and Threshold Voltage ........................................ 500 12.7.2 Inbuilt Swept Gain ........................................ 500 12.7.3 Adaptive Threshold ...................................... 501 12.7.4 Operator’s Gain Control ............................... 502 12.8 Radar Diversity .............................................................. 503 12.8.1 Principles ..................................................... 503 12.8.2 Criterion for Polar Diagram Decorrelation ............................................... 504 12.8.3 Criterion for Precipitation Clutter Decorrelation ............................................... 504 12.8.4 Space Diversity ............................................ 505 12.8.5 Swerling Case 3b; Case 1 Target Observed by Dual-diversity .......................... 506 12.8.6 Receiver Combinations ................................ 506 12.8.7 Combination Performance ........................... 509 12.8.8 Practical Problems ....................................... 509 12.9 Detection of Active Targets ........................................... 510 12.9.1 RTEs and Superhet Racons ........................ 510 This page has been reformatted by Knovel to provide easier navigation.

xxviii

Contents 12.9.2 Racons, etc., with Crystal-video Receivers ..................................................... 511

12.10 Practicalities ................................................................... 512 12.10.1 Sidelobes and Axial Ghost Echoes .............. 513 12.10.2 Roll and Pitch .............................................. 514 12.10.3 Wave Screening .......................................... 515 12.10.4 Actual Target Fluctuation ............................. 517 12.10.5 Losses ......................................................... 517 12.10.6 Anomalous Performance with Small Targets ........................................................ 517 12.11 Summary ....................................................................... 518 12.11.1 Targets ........................................................ 518 12.11.2 Noise ........................................................... 518 12.11.3 Precipitation ................................................. 519 12.11.4 Sea-waves ................................................... 519 12.11.5 Detection Strategy ....................................... 520 12.11.6 Display Accuracy ......................................... 520 12.11.7 System Integration – Diversity ..................... 520 12.12 References .................................................................... 520

13. Accuracy of Position and Track ................................ 523 13.1 Introduction .................................................................... 523 13.1.1 The Need to Consider Accuracy .................. 523 13.1.2 Display of Target Information ....................... 524 13.1.3 Sources of Error ........................................... 525 13.2 Forms of Error ................................................................ 526 13.2.1 Absolute and Relative Error ......................... 526 13.2.2 Systematic Error .......................................... 527 13.2.3 Random Error .............................................. 529 13.2.4 Latency ........................................................ 530 13.2.5 Quasi-random Error ..................................... 532


Contents

xxix

13.3 Errors in Terms within Radar Performance Calculations ................................................................... 532 13.3.1 Introduction .................................................. 532 13.3.2 Transmitter Hardware Losses ...................... 533 13.3.3 Service Loss ................................................ 533 13.3.4 Receiver Hardware Losses .......................... 534 13.3.5 System Processing Losses .......................... 535 13.3.6 Point Target Responses .............................. 536 13.3.7 Extended Target RCS .................................. 537 13.3.8 Scanner Rotation ......................................... 537 13.3.9 Environmental Conditions ............................ 537 13.4 Accuracy of Calculations Leading to SNR or PD ........... 539 13.4.1 Approximations within Calculations .............. 539 13.4.2 Radar Comparisons ..................................... 540 13.4.3 Mounting Heights ......................................... 540 13.5 Plot and Track Accuracy ............................................... 541 13.5.1 Instrument Errors ......................................... 541 13.5.2 Ship Motions ................................................ 541 13.5.3 Scan Plane Tilt Errors .................................. 542 13.5.4 Effects of SNR and Bandwidth on Plot Accuracy ...................................................... 544 13.5.5 Plotting Aid Prediction Accuracy .................. 545 13.5.6 Manoeuvres ................................................. 548 13.5.7 Identity Swap ............................................... 550 13.6 Combining Data from Multiple Sensors ........................ 552 13.6.1 Shipborne Radars ........................................ 552 13.6.2 Coastal Surveillance and VTS – Simple System ......................................................... 554 13.6.3 Autonomous Radar Heads with Trackformers ........................................................ 554 13.6.4 Central Track-former or Plot Extractor ......... 555


xxx

Contents 13.7 References .................................................................... 555

14. Spreadsheet Calculations .......................................... 557 14.1 Introduction .................................................................... 557 14.2 Passive Point Targets: Page 1 ...................................... 558 14.2.1 General Arrangement .................................. 558 14.2.2 Title Panel .................................................... 560 14.2.3 Transceiver Panel ........................................ 560 14.2.4 Scanner and Feeder Panel, and Table S2 ................................................................ 561 14.2.5 Range Bracket Panel ................................... 562 14.2.6 Target Panel ................................................ 563 14.2.7 Operator Panel and Table S1 ...................... 563 14.2.8 Environment Panel ....................................... 564 14.2.9 Results and User Panels ............................. 565 14.3 Geometry Panel ............................................................. 566 14.3.1 Layout .......................................................... 566 14.3.2 Establishment of α and R Series .................. 567 14.3.3 Scanner and Target Heights ........................ 567 14.3.4 Angles and Effective Scanner Gain .............. 568 14.4 Environmental Effects .................................................... 568 14.4.1 Diffraction Region ........................................ 568 14.4.2 Interference Region Multipath ...................... 568 14.4.3 Transition Region Multipath ......................... 569 14.4.4 Overall Multipath Factor ............................... 569 14.4.5 Atmospheric Loss ........................................ 569 14.5 Signals at the Radar Receiver, Single Pulse ................ 569 14.5.1 Effective Mode ............................................. 569 14.5.2 Noise and Swept Gain Floor ........................ 570 14.5.3 Precipitation Clutter ..................................... 570 14.5.4 Sea Clutter ................................................... 570


Contents

xxxi

14.5.5 Total Noise and Clutter ................................ 571 14.5.6 Echo ............................................................ 571 14.6 Main Beam Detection, Multiple Pulses ......................... 571 14.6.1 Pulses Integrated ......................................... 571 14.6.2 Integration Gain ........................................... 571 14.6.3 Swerling Case 0 ........................................... 571 14.6.4 Swerling Case 1 ........................................... 572 14.6.5 Swerling Case 3a ......................................... 572 14.6.6 Chosen Case Performance .......................... 572 14.6.7 Event Labels ................................................ 572 14.6.8 Results Panel ............................................... 573 14.7 Sidelobes ....................................................................... 573 14.8 Graphs ........................................................................... 574 14.8.1 Chart Construction ....................................... 574 14.8.2 Chart 1, Detectability ................................... 575 14.8.3 Chart 2, Geometry ....................................... 575 14.9 Extended Passive Targets ............................................ 576 14.9.1 Spreadsheet Page 1 .................................... 576 14.9.2 Remainder of Spreadsheet .......................... 576 14.10 Active Point Targets ...................................................... 578 14.10.1 Target Types ................................................ 578 14.10.2 Radar Auxiliary Racon Channel ................... 580 14.10.3 Device Antenna ........................................... 580 14.10.4 Device Characteristics ................................. 580 14.10.5 Device Interrogation Panel ........................... 581 14.10.6 Device Response Panel ............................... 582 14.10.7 Remaining Matrix Panels ............................. 582 14.10.8 Results Panel ............................................... 583 14.10.9 Charts .......................................................... 583 14.11 References .................................................................... 584


xxxii

Contents

15. Worked Examples ....................................................... 585 15.1 Deep-sea Ship Viewing Ships ....................................... 585 15.1.1 Nine Gigahertz Band, Small Craft Target .......................................................... 585 15.1.2 Three Gigahertz Band, Small Craft Target .......................................................... 594 15.2 VTS Installation .............................................................. 594 15.2.1 Scenario ...................................................... 594 15.2.2 PD Variation with Range; Effect of Scanner Height ............................................ 594 15.2.3 Scanner Aperture ......................................... 598 15.2.4 Feeder ......................................................... 600 15.2.5 Atmospheric Refraction ................................ 600 15.2.6 Coaster ........................................................ 603 15.2.7 Sidelobes ..................................................... 603 15.2.8 Purchase Specification ................................ 603 15.2.9 Site Acceptance Tests ................................. 607 15.3 Small Craft Radar .......................................................... 608 15.3.1 Detection of Cliffs ......................................... 608 15.3.2 Cliff Height ................................................... 609 15.3.3 Encounter with a Coaster ............................. 610 15.4 Active Targets ................................................................ 610 15.4.1 Detecting a Buoy Racon .............................. 610 15.4.2 Detecting a Radar Target Enhancer ............. 613

16. Future Possibilities ..................................................... 615 16.1 Introduction .................................................................... 615 16.2 The Drivers for Change ................................................. 616 16.2.1 Customer Requirements .............................. 616 16.2.2 Regulatory Change ...................................... 617 16.2.3 Cost Effectiveness ....................................... 619


Contents

xxxiii

16.2.4 Environment ................................................. 619 16.2.5 Technology .................................................. 620 16.3 Hardware Developments ............................................... 620 16.3.1 Transmitters ................................................. 620 16.3.2 Scanners ..................................................... 622 16.3.3 Digitisation ................................................... 623 16.4 Processing Enhancements ............................................ 624 16.4.1 Moving Target Indication .............................. 624 16.4.2 Long Pulses ................................................. 624 16.4.3 Pulse Compression ...................................... 625 16.4.4 Continuous Wave Transmission ................... 626 16.4.5 Target Profiling ............................................ 627 16.4.6 Monopulse ................................................... 630 16.5 Integrated Systems ........................................................ 631 16.6 Infrastructure and Implementation ................................ 632 16.7 Other Uses of Radar for Commercial and Leisure Shipping ......................................................................... 633 16.8 In Conclusion ................................................................. 635

Appendices Appendix A1: Glossary ............................................................. 637 Appendix A2: Statistics Details ................................................ 647 A2.1

Log-normal Distribution ................................ 647

A2.2

Rayleigh Distribution .................................... 647

A2.3

Ricean Distribution ....................................... 648 A2.3.1 Noise ................................................ 648 A2.3.2 Signal ................................................ 650

A2.4 Solution of Eq. (12.8) ........................................... 651 A2.5 Weibull Distribution .............................................. 652 A2.6 References .......................................................... 652

Index ................................................................................... 653 This page has been reformatted by Knovel to provide easier navigation.

Chapter 1

Introduction 4

It is on men that safety at sea depends and they cannot make a greater mistake than to suppose that machines can do all their work for them.' Mr Justice Cairns, giving judgement in the Trentbank-Fogo case, 1967, quoted in A. N. Cockcroft and J. N. F Lameijer, A Guide to the Collision Avoidance Rules, Stanford Maritime, London, 1976, p. 39

1.1

Purpose and scope

This introductory chapter explains the book's aims and methods, introduces the persons who operate radar, gives a brief historical background and outlines the regulatory framework under which marine radar is used.

1.1.1 Purpose The art, science and skill of the navigator is to get a ship from A to B without hitting anything. Ships come in many shapes and sizes, Figure 1.1, from pleasure yachts to half-million tonne tankers. A and B may be berths in harbours, but B may be a pilot cutter or a shoal of fish. Among the things to be avoided are coastal features, other vessels, heavy flotsam and ice. Radar is an essential tool used to locate these hazards, assisting the navigator to make timely manoeuvre decisions. Radar, an acronym for radio detection and ranging, detects objects of interest by transmitting radio signals in known directions from a narrow-beam antenna or scanner which scans the horizon, then timing the instants of reception of returned echoes from these 'targets'. (This Second World War term dates from development of radar for gunnery control and other military tasks; like much of the early jargon, it has stuck.) Each detected target is displayed map wise at its correct range and bearing. Additional to the anti-collision task, prudent seamen also still use radar to cross-check their position against known shore targets, despite the advent of satellite navigation systems as the prime onboard position finder. Ashore, vessel traffic service (VTS) radars depict the traffic situation in and around busy harbours and traffic lanes, and

Figure 1.1

Ships come in all sizes

range surveillance radars check that offshore gunnery ranges are clear to commence firing. The radar's first task is to pick out targets against a background of unwanted electrical fluctuations within the radar receiver and unwanted reflections from objects of no interest to the observer, such as waves and rain. In the jargon, targets must be detected in presence of noise and clutter. Only when this has been done can the radar go on to display target range and bearing or generate tracks of the target's movement to provide the operator with useful information. Much of this book treats the technical circumstances enabling a target to be displayed but one must never forget that even the finest radar is merely a tool which can be ignored, misused or misunderstood. It is always up to the operator to decide whether and how to use the radar and its information. The human-machine interfaces are the radar controls and the display screen. We shall step outside the realm of electronic engineering when considering how operators should utilise radar when performing their safety-related tasks, but steer clear of purely navigational matters, for which readers should turn to specialist books, such as those by Burger [1] for deep-sea ships, Bole and Dinelley [2], which concentrates on plotting aids and Wylie [3], which though old and out of print, remains surprisingly relevant in many respects, with many illustrations of radar displays of targets and clutter and much observational experience soundly based on theory. See Bartlett [4] for small vessels. The present book stems from a paper published in the Journal of Navigation [5]. It is primarily offered to those, perhaps neither radar specialists nor mariners, who need an understanding of how well civil marine shipborne and shore-based radars are likely to detect their targets under practical conditions. Targets may be 'natural' obj ects such as ships and coastlines which happen to reflect radar echoes, or may be specially prepared devices intended to return good radar signals. These include passive radar reflectors, racons and radar target enhancers (RTE), the latter two being secondary radars, speaking only when spoken to, and hence 'active' targets. The book discusses all aspects of the detectability problem and helps the reader answer such questions as: • •

Is higher transmitter power worth its cost to me? What is the best height for my scanner?

• • • • •

Which radar band should I choose? Would carriage of an RTE significantly improve detection of my craft? Which supplier's VTS proposal is best for my harbour? Do trials results match theoretical expectations? How does weather affect performance?

Radar is useless unless it can detect the targets of interest to the user, yet manufacturers in their data sheets rarely claim any specific detection ranges for their products. This is because the environment and many targets fluctuate in ways which are difficult to quantify or measure. Reports from seafarers (e.g. as quoted by Bell and Starling Lark [6]) stress the variability of observed detection range and the difficulty of detecting small targets in bad clutter; we shall explain why this is so. Although precision is impossible, we provide methods of calculating the likely detection performance of all the radar/target/clutter combinations likely to be met in practice, with spreadsheets enabling readers to calculate the performance of their own particular systems on a personal computer.

1.1.2 Scope We consider only radars used for civil shipborne navigation and collision avoidance and for VTS and related tasks such as sea surveillance of gunnery ranges, drug interdiction and sea traffic research studies. These all employ centimetric, non-coherent, pulsed, low pulse repetition frequency surface to surface surveillance radars with directional rotating common transmit-receive scanners. 'Non-coherent' means that our radars use only the amplitude of echoes, ignoring signal phase. In general, they also operate unambiguously, with only one pulse in play between radar and target at any instant. Other forms of radar exist, differing to lesser or greater extent, but are currently seldom used in marine contexts. Over the horizon radars and some others, although of course sharing the same underlying physical principles, differ so radically that only parts of this book apply directly. Much of the book is applicable to warship surface surveillance radar used for detection of surface targets, although we have completely excluded all the specifically military problems, such as jamming, which so dominate military radar design. Instead, we concentrate entirely on the civil field, where a modern treatment of detectability is lacking. Accuracy of positioning and tracking, which demands good detectability, is discussed towards the end of the book. The many other important radar qualities, such as size, cost and ease of use, are considered only where they influence detectability. The linked components of the radar - transceiver, scanner, display - are frequently referred to as a system. We however prefer to treat the whole radar as part of a wider system which also contains the other main interacting elements: the marine environment, the target and the operator. We point out some of the problems facing designers and indicate solutions. Likewise, we hope better understanding of the factors in play will help operators get the best from their equipment, and so contribute something to the safety of life at sea.

1.2

Radar users and uses

There are many specialist users such as warships, oil industry support vessels, buoy tenders, search and rescue craft and coastal surveillance systems. But the main operating personnel, whom we shall call operators, are probably associated with the following.

1.2.1 Merchant ships About 96 per cent of the world's international trade, some 6 billion tonnes per year, is transported in 35 000 or more merchant ships. Their radars are operated by the master, officer of the watch (OO W) and, if embarked, the pilot. These officers primarily use the radar or radars as an important navigational tool to do the following. 1. Assess the traffic situation - the position and tracks of other vessels, usually employing an Automatic Radar Plotting Aid (ARPA) or the simpler Automatic Tracking Aid (ATA); anticipate likely traffic movements, and make timely manoeuvre decisions under the Collision Regulations to give a safe clearing range of typically 1.5-4 km. The assessment may be that own ship is the 'stand on' ship under the regulations, the decision then being usually to maintain course and speed, keeping a close eye on the target's manoeuvres. Accurate tracking demands particularly good detection performance. 2. Monitor movements of other shipping for collision avoidance. 3. Monitor own ship's progress relative to sea-marks or coastal features, particularly in port approaches. Coastal echoes can be difficult to interpret, so racons or reflectors are used to pinpoint otherwise radar-inconspicuous lighthouses and buoys. 4. Detect ice, uncharted wrecks or other obstructions. 5. Rendezvous with pilot cutters, etc. 6. Maintain anchor watch, both for own ship dragging and for movements of other vessels. 7. Independently confirm position data provided by specialist instruments such as a global navigational satellite system (GNSS), currently comprising the [differential] global positioning system ([d]GPS, operated by the United States) and [differential] global navigation satellite system ([d]GLONASS, operated by the Russian Federation), which interpret data obtained by radio down-link from constellations of special-purpose satellites. Both GPS and GLONASS form part of the global maritime distress and safety system (GMDSS) and will be supplemented or superseded by later satellite chains such as Galileo. Lang [7] has published an interesting discussion of satellite reliability. Satellite signals are weak enough to be vulnerable to certain radio and television transmissions. Fourwatt jammers, available to terrorists on the Internet, apparently can jam to over 200 km. Worse, they may spoof receivers into indicating false position. It therefore remains a basic tenet of seamanship, as well as being a legal requirement, to use all available navigational aids for position finding. Well-found passenger

ships have grounded through sole reliance on very precise (but faulty) satellite navigation, ignoring the more woolly but independent radar coastline echo. 8. Make landfall. Since the advent of satellite navigation, this long-range task has lost some of its former importance. The relationship between radar suppliers and deck-officer operators is often tenuous. The radars may be procured by the shipowner, owner's purchasing manager, ship management company or shipbuilder, perhaps as a just-compliant product within a third party's overall bridge electronics deal rather than on technical merit. Repair and maintenance is perhaps in the hands of independent contractors, and the operators may be provided by a manning or ship management agency. One unfortunate result is that designers receive insufficient feedback on how well their products actually perform in the rough and tumble of actual service, rather than under controlled laboratory test conditions. 1.2.2

Leisure craft

Beside general navigation, the skipper or helmsman operates radar for obstruction avoidance, monitoring position of competitors when racing and sometimes to detect sea or precipitation clutter - to find smoother water, fairer weather or a good racing wind. Special radars have evolved for leisure craft. 1.2.3

Fishing vessels and small commercial

vessels

The watchkeeper is usually the skipper or mate, who operates the radar for most of the above tasks. In addition fishing vessels have to detect dan buoys which mark nets, monitor activities of other fishing vessels, perhaps hope to detect flocks of birds feeding on fish and use clutter returns to help keep an eye on the weather. The bigger yacht radars are often also fitted to small commercial vessels such as tugs and harbour workboats which are too small to have to carry radar within the international Safety of Life at Sea Convention (SOLAS, Section 1.4.5) but which choose to do so for operational convenience and safety. The International Maritime Organisation (IMO) has produced guidelines on appropriate performance for two radar sizes. 1.2.4

High speed craft

Collision avoidance is usually the first priority for fast ferries and other high speed craft (HSC). They use slightly modified conventional marine radar, augmented by night-vision infrared optical sensors for waterlogged obstructions which are poor radar targets. 1.2.5

Vessel traffic services

VTS systems provide a service to shipping, while technically similar vessel traffic management and information services (VTMIS) provide vessel movement data to

Figure 1.2

Dover Maritime Response Co-ordination and Control Centre (MRCC), UK Maritime and Coastguard Agency. On 80 m cliff commanding extensive views of the English Channel. Takes data from radar outstation at Hastings. Operates in conjunction with Port of London Authority and French CROSS radar networks. Reflector scanner operating in dual frequency diversity mode at 9GHz. Eight workstations, three being dedicated to emergency responses. Reproduced by permission of UK Maritime and Coastguard Agency, Norcontrol-IT and Easat

the port management. For our purposes we shall lump them together. VTS operators, sometimes called watchstanders, use radar to gain awareness of the traffic situation, confirm manoeuvres and positions reported-in by radio or by the radiobased automatic identification system fitted to all ships over 300 gross tons (AIS; from 31 December 2004) and maintain tracks on all significant targets within the surveillance area. At the shorter ranges, ships' aspect is often of considerable interest in confirming reported manoeuvres. Moves are afoot in IMO to introduce long range identification and tracking of ships by AIS for security purposes, which may necessitate some form of integration with VTS radar displays. An increasing number of systems akin to VTS are being installed to monitor shipping movements within traffic separation schemes (TSS) for safety purposes. Figure 1.2 shows one such station and Figure 1.3 shows a typical tower-mounted scanner. At the other end of the scale, coastal surveillance radars are used by coastguard and voluntary organisations to keep a safety watch on inshore craft near popular leisure resorts, particularly where currents can so often cause problems to the inexperienced,

see Figure \A(a)-(c). 1.2.6 Military applications For general navigation, in naval parlance Marine and Pilotage (M&P), many warships carry navigational radar generally similar to those on merchant ships. The radars we shall describe are devoid of any form of anti-jamming facilities (electronic protection, formerly called electronic counter-countermeasures, ECCM) and are unsuited to warfare. However, outfits similar to VTS and marine radars are used for safety surveillance of coastal gunnery and missile-firing ranges, and although little publicised,

Figure 1.3

High gain reflector scanner for sea surveillance service at 9GHz. Inverse cosec2 type, aperture 5.5 m, gain 4OdBi, switchable circular and horizontal polarisation. Steel tower also carries transmitterreceivers and communications equipment, plus infrared and CCTV cameras. Reproduced by permission of Easat Antennas Ltd, Stoke on Trent, UK

increasingly for drug, intruder and piracy interdiction by coastguard or gendarmerie services. The majority use frequencies in or near the marine 9 GHz band. Equipments vary from powerful (^250 kW) sets with massive reflector scanners derived from military practice and displaying in a VTS-like range control centre, down to the smaller deep-sea ship sets or even yacht radars, deployed in small rough-terrain vehicles. Performance can be predicted from the following chapters, but we shall not cover the specialist precision tracking pulse or frequency-modulated (FM) radars which follow the flight of the projectile and of its sub-munitions.

1.3

The past and future

1.3.1 The history of marine radar Some historical knowledge may help us understand why things are done as they are. After the First World War, liners were getting bigger and faster; would there be another Titanic disaster? The ship's whistle was acknowledged to be inadequate as the primary anti-collision aid in fog - despite the old Mauritania's whistle, reputed of 12miles range, deafening the young author when sounding the Friday 'knocking-off' time at the BT-H Works at Rugby. Strategic coastal lighthouses started to sport lights and fog signal emitters of heroic size. By the 1930s, the technology of short-wave radio had matured. Several countries continued Guglielmo Marconi's pioneering experiments in target detection by radio, particularly aimed at marine collision avoidance. It was realised that to cover surface targets, the best wavelengths were a few centimetres. These 'microwaves' were very short indeed by the standards of the day and barely

Figure 1. 4

Small 9GHz marine radars on surveillance duty. Sea Safety Group volunteers operate an expanding chain of coastal stations around the UK coasts. All Illustrations reproduced by permission of Captain A. R Starling Lark and Sea Safety Group, (a) Watchroom ofSSGRedcar Station, North-east England. A Furuno radar (left) augments the visual lookout. Combination with afluxgate compass speeds reporting of exact latitude and longitude of casualties to the Search and Rescue services, to which the fully trained volunteers are officially accredited. Roofmounted scanner at 40 m above sea level has 15 nmi horizon range and can detect target as close as the adjacent beach, (b) Viewfrom the watchroom towards the busy Tees Bay with its commercial shipping, (c) Twin displays. SSG Great Yarmouth Station. Quite small radars may suffice for inshore safety surveillance. Furuno 1832 radar, 4JcW transmitter power, 60 cm scanner. Feeds two 10 inch rectangular monochrome raster-scan displays. One observer can quickly guide Royal National Lifeboat Institution lifeboat to a casualty while a colleague maintains general surveillance, essential when sudden bad weather catches many leisure craft unawares

practical with the available technology. An experimental centimetric apparatus on the French liner Normandie was able to detect presence of ships at several miles range shortly before that great ship was destroyed by fire, and Radar Type XAF was at sea from 1938 in USS New York, but lack of transmitter power stymied progress.

Figure 1.4

Continued

Meanwhile the storm gathered over Europe. Britain, fearing airborne bombing and invasion, hastily and secretly set up a shore-based air surveillance system, constrained to conventional radio wavelength (~ 12 m) by the power problem. These Chain Home radars, described with a good engineering outline by Latham and Stobbs [8], resembled broadcast radio transmitter stations, with their huge static wire antenna arrays. They drew on nascent television technology. Immediate success in the Second World War triggered concerted research into the crucial need for powerful microwave generators. Necessity is the mother of invention and a superb solution was found with remarkable speed. Building on low-power cylindrical split-anode magnetrons developed in Japan, the cavity magnetron of 1940 opened the way to practical centimetric radar, first on fighter aircraft and then warships. Submarine periscopes became detectable as early as 1943. Perhaps exceeded in technological effort only by atomic energy and code-breaking, wartime Anglo-American radar research yielded an excellent understanding of basic principles. Declassified before the Cold War, the work was published around 1950, notably in the 28-volume MIT book series,1 much of whose content is still valid today. Late in the War thoughts turned to peacetime uses and the British were able to write a confident design aim for 'Post War Radar', including the first commercial marine radars. As early as May 1945, a 9GHz prototype navigational radar Type 268 was demonstrated [9] to civil marine interests aboard HMS Pollux, using a submerging submarine, HMS Umbra, as a variable-sized target - the wheel had turned full circle. The first commercial (1946) marine radars typically came complete with own cabin and roof-mounted scanner. Initially they were not very reliable and it took time for deck officers to accustom themselves to the strengths and limitations of this radically new aid to navigation. Nevertheless, the basic concept was sound,

1

Massachusetts Institute of Technology Radiation Laboratory, McGraw-Hill. Some volumes have been re-published by IEE in UK and all are available in CD-ROM form from McGraw-Hill.

early problems were gradually beaten and radar became mandatory for all ships. Wavelengths and frequencies are discussed in Chapter 2, but we mention here that frequencies around 3 GHz, wavelength 10 cm (S band, 3000MHz), was found best for detection in severe rain, in other conditions 9 GHz (3 cm, X band, 9400 MHz) being preferable. Some ships got the best of both worlds and carried both. Early suppliers were mainly large electrical firms who had been active in wartime radar. We shall not often mention individual firms but must make an exception for Decca (now Northrop Grumman Sperry Marine), who later deservedly won a pre-eminent position. Their war work included the Decca Navigator, but they did not enter the radar market until 1950. Until the late 1960s, purely analogue circuits were used, the raw echoes being presented on a cursive plan position indicator (PPI) using a cathode ray tube having a dim monochrome long-persistence phosphor. Operators had to draw tracks representing the movement of each target by grease-pencil on the Perspex face of a reflection plotter. Radars of those days contained several electro-mechanical devices - motors, relays, etc. - and the only semiconductors were a few rectifiers and the microwave detector 'crystals'. The hard work was done by about 50 valves (thermionic tubes in the United States, where the anode is known as a plate). Each valve was supported by a couple of dozen passive components, mainly resistors, capacitors and inductors, hand-soldered to insulating tags, and all carried on metal trays, connected by cable bundles. Each valve anode consumed about 2.5Wat250V and its heater dissipated another 2 W. The total heat was considerable and the dust attracted by the high voltage could cause arcing failures. Digital technology was in its infancy. Hardware meant screws. Software? What have woolly jumpers to do with radar? The term did not exist. Detail design by pencil, paper and sliderule was laborious and of variable quality, necessitating much 'cut and try' prototype testing. In 1977, after a spate of accidents causing pollution, political pressure caused the United States Coast Guard to issue, after discussion, regulations requiring all ships entering US waters to carry and use a collision avoidance system, to include continuous evaluation of the echoes of all ships posing a collision risk. This demarche quickly resulted in the international adoption of ARPA, the computer-based automatic radar plotting aid so widely used today. The remainder of the radar soon went solid state, although retaining a few analog circuits. Displays now often carry chart material from an electronic chart system (ECS).

1.3.2 Secondary radars Ship superstructures tended to be angular. To a radar engineer they were corner retroreflectors riveted together, so were inherently good targets, helping to give the early sets useful range. From the first it was realised that lighthouses ought to be made radarconspicuous, using transponders called racons (radar beacons), which early British experiments showed to be superior to ramarks radar markers. After initial setbacks, the first chain went into regular service around the British Isles in the late 1960s. Early sets weighed some 300 kg and consumed between 45 and 450 W, see Figure 1.5, but advent of solid-state electronics soon brought weight below 20 kg and consumption

Figure 1.5

Early 9GHz racons. (a) Bell Rock lighthouse. This historic structure, which first exhibited its light on 1 February 1811, carried one of the first racons to enter regular service, 1968. (b) Lighthouse engineer inspecting antenna. Transmit and receive full-height WG16 waveguides, four slots giving ±10° elevation beamwidth, flares giving omnidirectional azimuth response ±2dB, gain 7dB. Perspex X/2 radome. Reproduced by permission of the Northern Lighthouse Board, (c) Circuits rack. Duplicated transistorised receive-transmit units. Tuneable magnetron transmitters. Automatic monitoring and changeover unit above. Power consumption 45 Wfrom diesel generator. Sub-units transportable by ship's boat. Reproduced by permission of the Northern Lighthouse Board

Figure 1.6

Early low-power racon. GEC-AEISea-Watch 300; here in transponder duty on support ship s mast, 1973

to 1W, extending use to buoys; Figure 1.6. The market is well under 1000 a year, so racons remain rather costly. According to ITU,2 the world population is about 6000, of which rising 60 per cent are dual band, the remainder being 9 GHz types. In the 1980s racon technology was used as a basis, initially in Japan, for search and rescue transponders (SART) for the specialist task of marking liferafts. Being a mandatory carriage requirement, some 50 000 are carried by shipping, although it is hard to find evidence that they have saved many lives. The echoes of small Craft have for long been augmented by metallic reflectors, which are necessarily rather bulky. Active reflectors - containing electronic circuits have now appeared, called radar target enhancers (RTE). Problems remain, particularly provision of adequate radar cross section for heeling yachts. The potential user base is very large, exceeding that for small-craft radar, and prices are falling as products becomes better established and the regulatory authorities encourage carriage.

1.3.3 VTS Progressive port authorities quickly adapted ships' radar to monitor shipping movements from shore, initially to regulate traffic during and after fog. Although marine radars are still sometimes used for this task, 'harbour radar' has evolved into a specialist VTS discipline. Powerful radars with big scanners feed extensive data-handling adjuncts. Stations may have to combine echoes received by land-line or radio link from a dozen or more remote radar heads, and add data from other sources such as closed circuit television and shipping databases to provide the operator with full situational awareness of the traffic. The market is small - perhaps 100 stations a year - and 2 International Telecommunications Union document ITU-R SE34(99)1 Annex 3 (SE(99)TEMP 171 revl). Compatibility studies between existing and proposed new radio services in the band 2700-3400MHz.

equipments are often custom-built to port requirements, so unit cost tends to be high. Developments are concentrated on data fusion from multi-head systems, with some convergence with air traffic control practice. Range surveillance systems are broadly similar to VTS. Argument raged for a long time whether VTS should control or advise. The author soon found that use of VTMS (M for management) was likely to stir such a hornets' nest that the term is banished from this book. IMO is harmonising3 the training and certification of VTS operators and supervisors. As already noted, there is a trend to colocate maritime rescue coordination centres (MRCC) with VTS stations to enhance the resources available to handle marine incidents.

1.3.4 The current generation of radars All large fishing vessels, and all ships within SOLAS - broadly, all merchant ships have to carry a 9 GHz radar. The bigger merchant ships have to have a second set, preferably at 3 GHz. It is remarkable that after half a century's development in a competitive international market the WW2 design concept is still followed, demonstrating fitness for purpose rather than complacency. Although there have of course been numerous improvements in detail, centimetric-wavelength short pulses are still generated by a magnetron and radiated by a rotating scanner as a narrow beam. The tiny echoes bounced back from targets are amplified in a form of radio receiver and displayed as a map representation of the area surrounding the radar. Range continues to be calculated from elapsed time and bearing from scanner pointing angle. Instead of functioning as a stand-alone device, shipborne radars now tend to be treated as units within an integrated navigation-aid system, linked together to form an integrated bridge system or IBS. Radar designers seized on computer technology as it developed, particularly for processing the signal delivered from the receiver. This has enabled use of colour raster-scan television-style daylight-viewing screens, capable of displaying auxiliary data such as track lines and alpha-numerics, culminating in a complete superimposed electronic chart. Ever more computing capacity is now being harnessed, primarily to improve detection and tracking of multiple targets in clutter. Radars are now seen as sensors within an integrated data system, whether on the bridge in an integrated navigation system (INS), at the VTS centre or at the range control building. Most big-ship radars are no longer supplied as stand-alone items, but as part of a complete electronics package. In all cases the overall aims are improvement of the operator's situational awareness and enhanced detection of weak targets. Marine and VTS equipments are simpler than some military radars, and very much cheaper. But they are not a poor relation. On the contrary; long continuous development in a fiercely competitive market gives the user choice of the optimal engineering solution for almost every requirement of performance, reliability, ease of use, size and price. The world market for deep-sea radar is only moderate - less than 25 000 a year. Technological development work is costly and radar improvements 3

IMO MSC Circular 1065, IALA standards for training and certification of vessel traffic services (VTS) personnel.

perforce ride on the back of mass produced items for communications, computers and television. At the other end of the scale, miniaturisation and price reductions have enabled smaller craft to benefit from radar, and a large specialist yachting market has developed, particularly in the United States and the Far East. There may be 4 about 30 000 of 3 GHz radars at sea, predominantly on large ships and certain large fishing vessels, and 800 000 at 9 GHz, on vessels of all sizes. Marine radar engineers, of course, keep fully abreast of developments in related fields. Current work programmes concentrate on integration of displays with electronic charting and with integrated bridge systems generally, which all make wide use of digital technology, and this task is by no means yet complete. Emphasis is being placed on improving the echo strength of small vessels, some travelling fast, using passive or active reflectors. Radar is beginning to be employed to determine wave information for routeing assistance systems, to find the optimal route to minimise voyage time while avoiding seas bad enough to cause cargo damage, particularly when containers are carried on deck, or even to hazard the vessel itself. Increasing pressure on the electromagnetic spectrum from telecommunications interests has recently forced the radar industry to pay more attention to unwanted out-band transmitted interference and further tightening of permissible emissions can be expected.

1.3.5 Future possibilities Technical advances, evolving operational spectral and other constraints, plus desire for new facilities may induce substantial design changes in the fairly near future. Professor Baker, who has been studying the possibilities, has very kindly, and bravely, contributed a concluding chapter reviewing a wide range of options for change. Some are evolutionary, continuing existing trends. More revolutionary re-design would discard much of the present 'pulse magnetron' configuration in favour of low power, long pulse modulated transmissions, active scanners, microwave data processing and other unfamiliar concepts. What will happen only time can tell. Such developments would demand extensive revision of IMO and other regulations, not only those relating to radar itself, but extending to SARTs, racons, RTEs and reflectors. If only for that reason, new concepts will not supersede conventional technology for at least a decade and equipment to the current concept will surely be around in a quarter of a century's time. The underlying laws of physics are eternal and well understood, so most of the content of this book will always remain valid, come what may. Irrespective of the form radar may eventually take, it will be more necessary to combine marine or VTS radar data with that gathered from other sources, particularly the emerging AIS system. Sollosi [10] gives a useful summary of the VTS function and the problem of fusion of radar and AIS data.

4

From ITU-R, IALA standards for training and certification of vessel traffic services (VTS) personnel.

1.4 The regulators 1.4.1 Overview Mr Kim Fisher gives a good outline of the development of marine radar and its regulation in the Foreword. At first, marine radar was seen as experimental and the whole merchant marine was far less closely regulated than today. Innovation flourished. When designs had settled down and it became obvious that radar was useful and here to stay, some of the leading maritime nations began to require new designs to be type-approved by their admiralty laboratories to national specifications. A manufacturer faced the wearisome and expensive grind of seeking approval to slightly differing specifications in the United Kingdon, United States, Germany and other states. Racon specifications tended to be written by the suppliers in detailed consultation with leading lighthouse authorities. Meanwhile, IMO (see Section 1.4.3) had been founded, initially as the Inter-Governmental Maritime Consultative Organization (IMCO). Nowadays a formal international regulatory system is well established, as we shall see. Ports and harbours differ widely in size, traffic, weather, legislative basis, affluence and navigational difficulty. Harmonisation of working practices is slowly being tackled internationally through the International Association of Marine Aids to Navigation and Lighthouse Authorities (IALA; see Section 1.4.6) and others, leading to closer standardisation of VTS equipment and procedures. Today's shipping industry certainly does not lack international regulation. The following summary giving the spheres of operation of the main regulatory authorities and instruments involved in radar issues only skims the surface; for more on marine regulation see Maclachlan [H]. The regulations are revised from time to time and readers should always confirm the current position. For example, at the time of writing (March 2004), IMO and IEC were radically reviewing the radar performance standards. 1.4.2

UNCLOS

The United Nations Convention on the Law of the Sea codifies international law and customs of use of the sea which have evolved over the centuries and sets down the rules binding States on international marine affairs. It covers such concepts as the right of innocent passage and defines the limits of coast States'jurisdiction. Changes are made within the IMO framework at Diplomatic Conferences of Contracting Governments. 1.4.3

IMO

The following sections benefit from advice kindly supplied by Mr Rob Andrews5 and Mr I. Eckert.6 The International Maritime Organisation, with headquarters in London, is the United Nations agency charged with regulating maritime technical matters, with 5

(UK) Maritime and Coastguard Agency. I. Eckert of the Bundesamt fur Seeschiffahrt und Hydrographie, Hamburg. BSH is the German Federal Maritime and Hydrographie Agency. 6

strong emphasis on safety of life. IMO is a sister of the International Civil Aviation Organisation (ICAO), and the two cooperate on air-sea rescue and other topics of mutual interest. The newer industry of aviation was closely regulated from inception, but people had been going to sea from time immemorial, working to rules and customs thrashed out piecemeal as problems arose. It is therefore natural for IMO to take a more consensual approach than ICAO, regulations usually only being made binding after the more advanced users have developed them as best practice. Speaking broadly, IMO is a club of over 160 member administrations (in general, Nation States). The International Chamber of Shipping and 50 or more other official and non-governmental accredited organisations having the privilege of observer status also contribute to its decisions, which always follow wide consultation and debate. IMO only does what members agree and cannot act on its own initiative. To get a change made, one must persuade an accredited body, such as the International Chamber of Shipping or one's Government, to table the matter at, say, IMO's Marine Safety Committee. If MSC agrees the question merits attention, it will instruct the appropriate sub-committee (on which the administrations are represented) to investigate; observers may be invited to speak on topics where they have specialist expertise and concerns. Most radar subjects fall to the Sub-committee on Safety of Navigation (NAV) but a few are more appropriately handled by other Sub-committees; maybe Communications and Search and Rescue (COMSAR), Design and Equipment (DE), responsible for hulls and fittings or even by the Legal Committee. The7 Navigational Safety and Maritime Security section, formerly the Maritime Safety Division, has traditional duties pertaining to the work of the sub-committees on NAV and on COMSAR, and has assumed responsibility for regulatory matters relating to the prevention and suppression of terrorism against shipping. Any administration or observer can circulate discussion papers, in practice usually after taking soundings of interested parties within their country or membership. Papers are then debated at a session of, say, NAV. Having reached consensus after perhaps a couple of sessions' work, NAV tables its reply to MSC. If it approves, MSC either amends current requirements or proposes a formal Assembly resolution, for adoption at the next IMO Assembly. These diplomat-level meetings are held every 2 years. This rather ponderous but democratic procedure gives all interested parties internationally the opportunity to consider fully the proposed measure and its side-effects. Adopted resolutions are recognisable from their numbering system, thus: A.222(12), meaning Assembly Resolution number 222, adopted at the twelfth Assembly - formerly roman numerals were used, e.g. A.222(XII). Resolutions take the form of minimum operational performance standards (MOPS) or carriage requirements. Having written the performance standard, ISO or IEC (see Sections 1.4.8 and 1.4.9) prepare test or technical standards.

1.4.4 National consultations Each state has its own way of forming its position on any topic before IMO. In the United Kingdom, the Maritime and Coastguard Agency (MCA) is responsible for This paragraph is reproduced from Seaways, The International Journal of The Nautical Institute, April 2002, 'Nautelex', Brian Bailey.

matters affecting marine safety. MCA is an executive agency of the Department for the Environment, Transport and the Regions - titles seem to change after every general election - whose ministers are of course responsible through parliament to the electorate. Two groups gather opinion. The Safety of Navigation Committee (UKSON) is responsible for policy and political issues. Its membership includes government departments, shipowners' and seafarers' representative associations and less formal bodies. The Marine Navigational Equipment (MNE) sub-committee handles technical matters, with membership drawn from shipowners, navigators, lighthouse authorities, seafaring trade union interests, equipment manufacturers and the training colleges. There is overlap and the committees liaise closely. This arrangement has stood the test of time and the author has always found it possible to get a fair hearing for a cogently expressed view. Operators frequently grumble that 'the powers that be' have foisted yet another inappropriate measure on them. The remedy is partially at least in their own hands; to make their views known through the channels outlined above. Communication has never been easier.

1.4.5

SOLAS and the Colregs

Most IMO assembly resolutions are incorporated within major IMO legal instruments, in particular SOLAS (sometimes written Solas). This International Convention on Safety of Life at Sea is binding on all Contracting States after ratification by a preset number of them. It has a number of chapters and is revised from time to time. Chapters 5 and 10 include the Carriage Requirements for radar and other on-board navigation equipment for ships and for HSCs, respectively. These define what must be carried on each size and class of ship, including the navigational radar. SOLAS also states if and when exceptions may be permitted by national authorities and defines specifications and type-testing procedures applicable to the equipments. Similarly the Convention on the International Regulations for Preventing Collisions at Sea, variously known as IRPCS, the collision regulations, Colregs, or the rules, is a mandatory set of 'rules of the road' for navigation of all craft, including requirements for full and appropriate use to be made of radar. Cockcroft and Lameijer [12] print and fully explain the Colregs.

1.4.6

IALA

The International Association of Marine Aids to Navigation and Lighthouse Authorities8 brings together services and organisations concerned with the provision of marine aids to navigation systems and allied activities including vessel traffic services, at sea and on inland waterways. It is responsible to IMO for matters concerning operation of aids to navigation such as lights and buoys, electronics and VTS matters being handled by its radionavigation and VTS Committees, respectively.

8

20ter rue Schnapper, 78100 Saint Germain-en-Laye, France, [email protected].

The General Lighthouse Authorities (almost invariably government departments) of most leading maritime states are members. Specialist organisations such as the International Association of Ports and Harbours are represented and most of the leading suppliers of lighthouse and VTS equipment are Industrial Members. Because harbours differ so widely and so many are state-controlled, international regulation of their activities has been fairly light. 1.4.7

Enforcement

IMO has no policemen. Enforcement of its instruments is entrusted to domestic legislation of the national Administrations adopting IMO conventions, through Flag State (in which the vessel is registered) and Port State (states visited by the vessel) controls. For example, the Colregs are given force of law in the United Kingdom by Statutory Instrument.9 It is the duty of Flag State administrations to ensure their shipping carries radar conforming to SOLAS requirements and that ships' officers are properly qualified. Classification Societies provide design, build and maintenance standards for shipping, primarily for insurance purposes, to answer that centuries-old question: Is this ship a good insurance risk - is she seaworthy? Among many other tasks, their surveyors need to assure themselves that the radar installation complies with IMO carriage requirements. 1.4.8

ISO

The purpose of the International Organisation for Standardisation is to issue internationally acceptable technical standards to facilitate world trade. It has over 100 member nations and over 180 technical committees and has published around 10 000 standards on all manner of things, although electrical equipment is generally handled by the IEC (see below). Membership structure is similar to that of IMO. ISO/TC-8 is the ISO Technical Committee on Ships and Marine Technology, responsible for design, construction, structural elements, outfitting parts, equipment, methods and technology, and marine environmental matters, subject to IMO requirements. Users are encouraged to feed back their experience into the standardisation process. TC-8 links IMO to the marine industry. Of its ten sub-committees, SC6 deals with navigation. 1.4.9

IEC

The International Electrotechnical Commission issues detailed test and technical specifications for electrical and electronic equipment. ISO or IEC, as appropriate, clarify IMO 's requirements, tie them in with related requirements of bodies such as the International Hydrographic Organisation (IHO, responsible for coordination of 9

Statutory Instrument SI 1996/75, Merchant Shipping Safety. The Merchant Shipping (Distress Signals and Prevention of Collisions) Regulations (HMSO, London).

nautical charts) and ITU (see below), and define methods of testing and required test results to harmonise with IMO performance standards, without extending the requirements. Older IEC specifications having three digit serial numbers have been renumbered by addition of 60000; for example, IEC936 becomes IEC60936:1999, the suffix indicating date of latest revision.

1.4.10 ITU As for any other radio device, radar transmissions are governed by the Radiocommunication Sector (ITU-R) of the International Telecommunication Union. This United Nations body regulates all classes of radio service to assure interoperability and prevent interference and has taken on former Comite Consultatif International de Radiocommunication's (CCIR's) responsibilities. Radar lies within the Radiodetermination Service. ITU-R allocates blocks of the radio spectrum to the various services, with limits on permissible out-of-band transmission and forms of modulation. It holds World Radio Conferences (WRC) or World Administrative Radio Conferences (WARC) every couple of years. Its regulations are administered by national regulatory authorities. Further details are given in Hall et al. [13]. There is considerable and useful overlap of delegates to IMO, ISO, IEC and ITU working groups. 1.4.11 National

regulations

Many IMO Instruments have to be backed by parliamentary approval and national legislation to gain legal force within the Flag or Port State. National regulations and approvals outside the IMO framework may also apply to some aspects of radar equipment and its use; for example siting and height of VTS scanner towers are often constrained by visual amenity considerations. Transmission licences are usually issued by national post telephone and telecommunications (PTT) authorities; in the United Kingdom by the Radiocommunications Agency, an executive agency of the Department of Trade and Industry; in the United States by the Federal Communications Commission (FCC).

1.4.12 National and supra-national groups; the European Community Many states have national standards organisations, for example, the British Standards Institute. Frequently their standards antedate ISO and IEC but have now usually been harmonised with the international equivalents. The national organisations, by a consultation and voting process, endorse draft IEC and ISO standards before enactment. A tendency is developing for regional organisations such as the North American Free Trade Agreement (NAFTA) and particularly the European Community (EC) to interest themselves in marine regulation, particularly of fishing vessels and their equipment. The EC has spawned further standards authorities, which publish the EN (European Norm) series of standards as follows (EN IEC standards are technically

identical to IEC standards): • • •

European Committee for Standardisation (CEN) European Committee for Electrotechnical Standardisation (Cenelec) European Telecommunication Standards Institute (ETSI).

After a parliamentary process, the EC imposes its will on member states by directives. One such10 lists many international testing standards for radar, SARTs and much else. Subject to derogations in special cases, directives have the force of law in the states. Domestic laws have to be amended to comply, directives overriding any conflicting national legislation. The European Marine Equipment Directive (MarED) harmonises procedures within member states. It permits independent laboratories to type-test marine equipment against relevant specifications and recommendations issued by bodies such as IMO, ISO, ITU, CENELEC and ETSI. Compliant equipment is identified by a wheelmark. Wheelmarked items are recognised by all member states, irrespective of the approving state, doing away with the former multiplicity of national tests. Subject to 'grandfather clauses' allowing certain existing equipment, ships flagged by member states are obliged to have wheelmarked obligatory navigational equipment, including the radars. Optional additional equipment may be carried, such as radar on vessels below IMO's minimum tonnage limit for obligatory radar carriage, currently 300 gt. The EC requires these equipments to comply with the R&TTE Directive, which includes ITU regulations. Within Germany, for example, SOLAS, the MarED and the R&TTE Directive have been made mandatory by inclusion within national law, their yachting radars only having to comply with the R&TTE Directive. The European Union (EU) has a Maritime Transport Directorate, (DG, TREN) and wishes also to upgrade its position as observer-only at the IMO. Current EU maritime policy concentrates on the enforcement by member states of international regulations and to fill the gaps in existing legislation. It also aims to make its waters the safest in the world. It remains to be seen how these aspirations will be received by the other IMO States. Following major shipping disasters in European waters, the EU has adopted very substantial packages of legislation to improve maritime safety and reduce pollution, and in 2003 created the European Maritime Safety Agency to contribute to the enhancement of the overall maritime safety system in the EC. Among its tasks will be to establish a Community vessel traffic and information system. The EMSA will also facilitate cooperation between the member States. For details see Seaways,11 March 2004, from which this paragraph is extracted.

1.4.13 The courts The final interpreter of the law is the lawcourt. Although criminal prosecutions are few, civil litigation is often used to determine who was to blame and should pay for marine 10

EC Council Directive 96/98/EC of 20 December 1996 (OJ No. L 46, 17.2.1997, p. 25) as amended. "Making European waters safer? The European Maritime Safety Agency programme for 2004." Seaways, the International Journal of the Nautical Institute, March 2004, plO. 11

accident damage. The courts' interpretation of all rules and regulations is governed by an accumulated body of national and international case law. In recent years, the thrust in many jurisdictions has been to stress the responsibility of senior management to provide appropriate tools for the job and to ensure by formal procedures that they are safely and correctly used by trained personnel. Imagine a fishing vessel (FV) has collided with a coaster. The evidence of its officer of the watch, confirmed by the voyage recorder, is accepted that although diligently observing the radar, which was correctly set for the severe sea clutter, the FV was undetectable. Apportionment of blame might depend on the court's findings on these questions. • • •

•

1.5

Was the radar capable of detecting the target? Ought the coaster owners to have known by how much the long feeder to the high scanner would degrade the radar's performance? Ought they to have known that this radar outfit with its small high scanner was unsuited to the small targets and rough weather prevalent in the coaster's trading area? Should the skipper have known that his inferior radar reflector, incorrectly mounted, would jeopardise his vessel's detectability?

The regulations

1.5.1 Radar for ships within SOLAS The following particularly clear overview of the main performance standards for marine radar, written by Mike Pope, of the radar manufacturer Sperry Marine cannot be bettered. It is reproduced with permission [14], with formal specification titles and IMO references added. Performance standards for marine radars are promulgated by the IEC. Historically, these performance standards have been published as separate stand-alone documents and I believe that a future task will be to combine them into a single performance specification. Herewith a brief description of the current standards. 1. IEC 60936-1, Maritime navigation and radiocommunication equipment and systems - Radar - Part 1: Shipboard radar - Performance requirements - Method of testing and required test results. This is the fundamental radar specification all manufacturers must meet (for equipment to be fitted on Solas vessels). It defines all of the important parameters that the equipment must comply with to achieve type approval. It defines the range scales to be offered (others may be offered, but it must include those specified), minimum range requirements, range and bearing discrimination, minimum antenna scan rate, azimuth stabilisation details, bearing scale details, range and bearing measuring tools and accuracies, range performance, display modes of operation and other specifications. (Pope later comments that IEC 60936-1 Annex D contains tighter emission regulations for radars in the 3 and 9 GHz bands to meet new ITU regulations. WRC 2003 is to consider, and probably tighten, the boundary between out of band emissions and in band peak equivalent power, PEP).

2.

3.

4.

5.

6.

7.

IEC 60936-2, Maritime navigation and radiocommunication equipment and systems - Radar - Part 2: Shipboard radar for high speed craft (HSC) - Performance requirements - Method of testing and required test results. This standard is, in effect, an extension of the above, and describes the additional requirements for radar which are to be fitted to HSC. The minimum range and range discrimination requirements are more demanding and the antenna rotation rate is higher (40 rpm minimum). This standard also details the scenarios that the associated ATA or ARPA must comply with. IEC 60936-3, Maritime navigation and radiocommunication equipment and systems - Radar - Part 3: Radar with chartfacilities - Performance requirements - Method of testing and required test results. This standard is new, published in 2002. It details the testing standards and test results required for radars with charting facilities. It also defines what information can be displayed: in effect, it is only selected parts of the system electronic navigation chart (SENC) that may be shown. The most important point to make here is that it is a radar, not a chart display system, and it is vital that the radar information should not be masked or degraded in any way when the chart information is added to the display. IEC 60872-1, Maritime navigation and radiocommunication equipment and systems - Radar plotting aids -Automatic radar plotting aids (ARPA) - Methods of testing and required test results. This standard details the minimum number of targets we have to track, the tracking accuracy to be achieved, alpha-numeric data to be displayed for the tracked targets, details on guard zones and acquisition zones, operational warnings, trial manoeuvre details, interfacing, symbols and other specifications. [Based on IMO Resolution A.823:1995, performance standards for automatic radar plotting aids (ARPAs).] IEC 60872-2, Maritime navigation and radiocommunication equipment and systems - Radar plotting aids -Automatic tracking aids (ATA) - Methods of testing and required test results. The ATA specification is very similar to that of the ARPA, except that the ATA has to track a minimum of 10 targets compared to the ARPA's 20. Also, for the ATA, trial manoeuvre and history dots are not required. IEC 60872-3, Radar plotting aids - Electronic plotting aids (EPA) - Methods of testing and required test results. This is the simplest of the three plotting standards. EPA is a manual plotting system. Again, the standard defines how many targets are to be manually plotted, how the information is to be displayed, symbols to be used, accuracy to be required and other specifications. IEC 60945, Maritime navigation and radiocommunication equipment and systems - General requirements - Methods of testing and required test results. This standard deals with issues such as environmental testing for heat, cold, humidity, vibration and corrosion. It also deals with electromagnetic emissions and susceptibility to electromagnetic interference, illumination of controls, compass safe distance, equipment manuals and acoustic noise.

IMO's 2004 radar review will doubtless lead to the amendment of IEC 60936 and IEC 60872.

1.5.2 Radar for craft outside SOLAS These radars, carried voluntarily, may comply with a recent performance specification, IEC 62252 EDl Maritime navigation and radiocommunication equipment and systems - Radar for craft not in compliance with IMO SOLAS Chapter V - Performance requirements and methods of test and required test results. Summarising, three classes of radar, A, B and C, are recognised and may use the 3 or 9 GHz bands. Scanner first sidelobes should not exceed -2OdB (class A) otherwise — 18dB. When mounted at 7.5m, with normal propagation and no clutter, the radars should pick out the following targets on 8 out of 10 scans: Ground rising to 60 m: Class A 9 nmi; classes B and C 5 nmi. Ground rising to 6 m: Class A 5 nmi; classes B and C 3 nmi. Radar reflector, RCS 400 m2 at height 7.5 m: Class A 5 nmi; classes B and C 3 nmi. Radar reflector, RCS 10 m2 at 3.5 m: Class A 2 nmi; classes B and C 1 nmi. Minimum ranges: Class A 50 m, class B 60 m, class C 75 m. Radar reflector, RCS 5 m2 at 3.5 m: Class A 1 nmi, classes B and C not applicable. In sea clutter a target of 200 m2 (class A) otherwise 400 m2 should be detected at 100 m to 1 nmi on 5 of 10 scans. Display effective diameter: Class A 150 mm, class B 85 mm, class C 75 mm.

1.6

Theory and calculations

1.6.1 Sources No book of this sort could be written without reference to several good textbooks such as those by Barton [15], Kingsley and Quegan [16] and Skolnik [17]. These and numerous papers treat detection as part of radar or communications theory. Our text references all sources of important quantitative data, but it is impossible to reference every qualitative statement, many of which have been absorbed by the author over the years. Readers needing more depth should go to the relevant textbook chapters. The textbooks are generally well indexed and contain extensive bibliographies, routing interested readers to the specialist literature, which is voluminous but often difficult for the layman. Unfortunately, most textbooks either generalise by including aircraft, military jammers and other problems of no interest to us, or demand deep prior knowledge of electronics and mathematics. We shall consider only factors likely to have some practical significance, mentioning matters of purely academic interest only where necessary as a step to solution of some practical problem. We have aimed always to give sufficient theory to highlight what actually happens, the conditions under which results are valid and the likely residual error in calculations, and have tried to be consistent in terminology. Readers wishing to brush up on their basic understanding of electronics may find Bishop [18] or Hagon [19] useful. Detectability depends on aspects of radar engineering, navigation, meteorology, oceanography and statistics. We have tried to give a straightforward account assuming no prior knowledge of these subjects. All of them abbreviate their common technical statements using jargon, which we shall explain as we go along. For example, the navigator might ask 'At what range should our X-band radar raise a panamax

bulker loaded to her WNA marks?' and the engineer might answer ' 12 miles assuming four-thirds Earth and RCS 4OdB square metres.' The value of this jargon is shown by the long-windedness of these technical sentences in plain speech: 4At what maximum range should our radar lying in the marine 9 billion cycles per second frequency band display the radar reflection of a ship whose size is the maximum allowable in the Panama Canal and designed for carriage of bulk cargo, when laden to the winter North Atlantic load-line mark on her hull?' and 'At 22 km, assuming the rate of change of refractive index with height of the atmosphere is such that if the Earth were assumed to have | its actual radius radar rays would travel in straight lines, and she reflects equivalently to a metal sphere of silhouette area 10 thousand square metres.' The more important jargon terms are defined in the Glossary, Appendix 1.

1.6.2 Mathematics and units We have tried our best to keep the inevitable mathematics of the calculations as simple as we can. This approach leads to a few differences from the standard treatment of some topics, indicated in the text. Some of the other possible treatments give slightly higher accuracy at the cost of more difficult mathematics, but the uncertainties surrounding the environment between the radar and its targets, as well as those within some of the targets, usually swamp any approximations of our approach. Refer to Chapter 13 for comments on accuracy of calculations. Wide use will be made of decibel (dB) notation, explained in Chapter 2, Section 2.1.7. Scientific writing uses SI (Systeme International des Unites) units,12 formerly called the rationalised metre-kilogram-second (MKS) system, whose base units are: length (metre, symbol m), mass (kilogramme, kg), time (second, s), electric current (ampere, A), temperature (kelvin, K = degree Celsius + 273.3); also amount of substance (mole, symbol mol) and luminous intensity (candela, cd), which do not concern us. The radian (rad) of plane angle and the steradian (sr) of solid angle are supplementary units. Derived units for all other physical quantities use the above in a manner which minimises constants of proportionality. Examples are the newton, the measure of force, dimensions m kg s~2, and the volt, the measure of electric potential, m2kgs"3A-1. We retain some everyday non-SI units: 1° = 27r/360rad ~ 0.001745 rad, 1 foot = 0.3048 m. The nautical mile remains in widespread marine use, including radar display scaling (although kilometres are preferred for river radar), and is often abbreviated n.m. but to avoid confusion with nanometres (10~ 9 m) we prefer nmi. 1 cable is 0.1 nmi, its use generally inferring an approximation. Relationships are: 1 nmi = 1 min of latitude. Napoleon's savants defined the metre as 10~7 the distance from the North Pole to the Equator, through Paris; by which 1 nmi — 107/(60 x 90) m = 1851.85 m. (The metre has since been redefined as the distance travelled by light in vacuum in 1/299 792 458 s and 1 nmi as 1852 m exactly). 12

Units and Symbols for Electrical and Electronic Engineering, an IEE Guide (Institution of Electrical Engineers, London, 1997).

If once upon a time a foot represented 0.01 s of latitude, the modern foot is 1.3 per cent short. The statute mile is 5280 ft, 0.869 nmi or 1.609 km. Our calculations will usually prefer km to nmi to minimise tedious conversion factors. Bearings are either True (relative to the North Pole) or relative to some stated reference such as ship's head (i.e. centreline). With wide use of gyrocompasses, Magnetic North is less used. A point (of the compass) is 360/32 = 11.25°, used by mariners for rough estimates. Grads, 400 to a circle, milliradians and circular mils (6400 to a circle) are not used in civil marine. We do not follow a forthcoming ISO standard, ISO 19018, which defines many navigational terms in a consistent manner. It includes the nautical mile (NM, but abbreviated as M on charts) as the fundamental length; 1 NM = 1852 m. 1/10 NM is 1 cbl (cablelength, also named cable). The unit of speed is the knot (kn): 1 kn = 1 NM/hr. The standard uses abbreviations RM, H up, C up, N up for relative motion, ship's head up, . . . course up, . . . north up of displays. For details see Junge,13 on which this paragraph is based. For convenience, we often use practical units; ranges in kilometres, wavelengths in centimetres, antenna beamwidths in degrees, transmitter powers in kilowatts, pulselengths in microseconds. But except where definitely stated, our formulae always express angles in radians, lengths (wavelength, range, etc.) in metres and times in seconds. That is, we use SI except where other measures are widespread - an example is rainfall rate, quoted in mmh" 1 rather than kgm~ 2 s" 1 . Always remember to make appropriate conversions', for example, in calculations 1OkW (10000 W) transmitter power must be written 104 W or preferably in scientific notation as 10 x 103 W, and 1.0° scanner beamwidth must be put as 0.01745 . . . rad. The basic units often give inconveniently large or small numbers, for example, frequency 60000000 s" 1 , or current 0.0007 A. These zeros and 'damned dots' are a fruitful source of error - the result of a calculation may be dead accurate apart from being a thousand times too big! Prefixes are applied every 103: giga (G) = 109, mega (M) = 106. The smaller multipliers use lower-case letters: kilo (k) = 103, milli (m) = 10~3, micro (|x = mu) = 10" 6 , nano (n) = 10~9, pico (p) = 10" 12 . Other multipliers in common use are the centimetre (cm), 10~ 2 m; decibel (dB), 10" 1 bel, and for atmospheric pressure the hectopascal (hPa), 102 Pa. Inadvertent use of mixed units is productive of error in calculations and unfortunately not all information sources clarify their units. The author has been caught out often enough to make no apology for insertion of units after equations - especially when non-SI - for avoidance of doubt, when purists would deem them unnecessary. Where no units are stated, SI units are to be understood. The electrical units - volt, amp, ohm, watt, farad, henry, etc. - form a coherent set within the SI system, so when we write V = IR we do not need to add that the answer is in volts when current / is in amperes and resistance R in ohms. The fly in the ointment is frequency, where 2n often sneaks in. Radian frequency (co = 2nf) merely

H. Junge, "Harmonisation of navigational terms. Synopsis of ISO/19018/Final/draft." Seaways, the International Journal of the Nautical Institute, April 2004 p26.

transfers 2TT to formulae involving wavelength, so we generally retain conventional (cyclic) frequency, generally referred to simply as 'frequency', / (Hz) and put up with a sprinkling of 27rs in expressions. We write log(jc) for the common logarithm log10 Qt), having base 10, of a quantity x; and ln(x) for the natural logarithm of x9 base e. So In (JC) is identical to log£(jc), where the Euler number e = 2.71828...; Iog10(jc) = 0.4343 . . . In (JC); ln(jc) = 2.3025... log(;c). Only when there is specific need to emphasise the base would we add the subscripts. Scaling of graphs within figures is always linear except when axes are specifically indicated as, for example, 'log scale'. Many of our graph axes run between non-zero quantities, with suppressed zero.

1.6.3

Basis of performance

calculations

Equipment manufacturers rarely divulge the exact strategies they use for the various steps of the detection process, particularly now that maintenance is by exchange of printed circuit boards or other lowest replaceable units containing high levels of functionality and many functions are carried out within custom-made, digital application-specific integrated circuits (ASICs) whose workings are not divulged. We therefore proceed by noting the performance available within the published 'data sheet' limits of transmitter power, scanner gain, prf, etc. and making reasonable allowance for shortfalls likely to arise in practical designs. The validity of the approach depends in part on the competitive nature of the industry; what can be done soon is done, and woe betide those firms who do not keep up!

1.6.4

Spreadsheet

calculation

The equations needed for calculation of system performance are presented in forms convenient for generation of personal computer (PC) spreadsheets. Chapter 14 gives full listings and operating instructions. Having entered radar, target and environmental parameters, the spreadsheets, available on the IEE website (www.iee.org), deliver results such as maximum detectable ranges and indications of how well detectability is maintained as range closes, with graphs linking such parameters as detectability and range. It is then easy to explore the effect of radar, environmental and target parameters on performance. This approach informs judgement of how worthwhile the various parameters may be in a given situation or the robustness of a configuration against clutter and other environmental uncertainties. The spreadsheets should also help design trials of radars and aids to detection for minimum error from unwanted environmental effects, which was not always possible in the past.

1.6.5

Approximate

methods

Full calculation is often complex and may not be justified for the task in hand, so we often include alternative approximate methods, sometimes using graphs. Rough approximations should not be despised, their uses include the following.

• • • •

1.7

Highlighting the major factors in play, separating the wood from the trees. Explaining principles to others. Getting 'orders of magnitude' for preliminary work. Not least, checking for blunders.

The layout of this book

The text assumes a working knowledge of elementary electro-technology. It tells the story of the detection of targets, setting out the factors in a logical sequence. To avoid harking forward, some early chapters summarise topics whose details come later. The calculation examples frequently included should not be taken out of context; extreme values or drastic simplifications are sometimes chosen to illustrate particular points under discussion, so calculated results may not apply to the complexities of real life. Where costs are quoted, they are broadly indicative 2004 values, at exchange rates £1 ~ $ U S 1 . 8 0 ~ € l . 5 0 . Chapter 2 qualitatively describes how marine, VTS and similar surveillance radars illuminate targets, stressing that the radar and scanner, the operator, the target and the environment work together as a system. Here and throughout, we give examples of typical values of frequency, losses and other parameters, which do not describe or endorse any particular make or model of equipment. Chapter 3 discusses reception of echoes and unwanted clutter, signal processing, detection and display. Readers with a good understanding of radar technology but coming fresh to marine work should note how the emphasis differs from defence and other radars, for example; there are no jammers and few other man-made impediments, but MTI technology is not appropriate. Chapter 4 describes what would happen in hypothetical 'free space' where the environment plays no part. The inverse-square law of schooldays physics is at the core of the radar range equation, used to calculate echo strengths. Chapter 5 looks at the influence of the environment on propagation of signals from the radar scanner to the target and back. As propagation depends on atmospheric factors and sea surface roughness, some elementary meteorological and oceanographic background is included. Although we speak of the 'sea', the surface might equally be that of a ship canal, river or fresh-water lake. Chapter 6 develops a multipath factor to describe how direct and indirect rays combine to form the resultant signal actually received from simple point targets at short and long ranges. The range equation is extended to include atmospheric and precipitation attenuation. Chapter 7 discusses the simple theory of reflection from insulators and conductors and then outlines the performance of small targets such as aid-to-navigation reflectors which approximate geometrical points. The effects of target tilt are included. Some examples are given of target pairs and their effect on the uniformity of reflection with viewing aspect. Chapter 8 describes active point targets, including racons, SARTs and radar target enhancers. The influence of target characteristics on the response received by the radar

is presented for each class of active target. Allowances are made for tilt and the passive echo of the host platform. So far the emphasis has been on point targets. Chapter 9 develops a multipath factor to cover the very important classes of extended targets such as ships and coastlines which are too big to behave like points, developing a method of calculation which accounts for the changing effective cross-section when the incoming target rises over the horizon, and if it exceeds scanner beamwidth and pulselength. Chapter 10 examines the radar cross section of ships etc., which is often very uncertain. Some of the values reported in the literature are reviewed, followed by an attempt to clothe the experimental results with an elementary theoretical justification. By the end of this chapter all the necessary information has been assembled for calculation of the mean echo strength of all classes of target, including variation with range, weather and the other environmental factors. Chapter 11 examines noise, precipitation and sea clutter, which compete with echoes to make detection more difficult. In Chapter 12, the detection process is shown to depend on fluctuations of echoes and on the noise and clutter background. Statistical analysis finds the probability of detection and of false alarms. Approximations are included, whose accuracy is appropriate to the inevitable uncertainties of actual target cross-sections, environmental parameters and inherent radar performance. Chapter 13 considers the effect of signal strength on positional accuracy and target tracking, with special reference to track formation using electronic plotting aids, and the particular problems faced by VTS and coastal surveillance systems. Chapter 14 introduces a method of calculation for all the factors in play, suited to spreadsheet calculation of probability of detection and many associated parameters on a personal computer. Chapter 15 contains worked case studies which highlight the factors of significance in representative practical situations. In Chapter 16, Professor Baker reviews future possibilities for improvement of marine radar. Appendix A1 is a glossary of specialist terms, while Appendix A2 augments some statistics detail of Chapters 11 and 12.

1.8

References

1 BURGER, W.: 'The radar observer's handbook' (9th (revised) edn.) 2 BOLE, A. G. and DINELLEY, W. 0.: 'Radar and ARPA manual' (Heinemann andNewnes, 1990) 3 Capt. WYLIE, F. J. (Ed.): 'The use of radar at sea' (Hollis & Carter for the Royal Institute of Navigation, London, 1952, 1st edn.; 1978, 5th (revised) edn.) 4 BARTLETT, T.: 'Radar afloat (official background reader to the RYA radar course)' (Fernhurst Books)

5 BRIGGS, J. N.: 'Detection of marine radar targets', Journal of Navigation, 1996, 49(3) 6 BELL, S. W. and STARLING LARK, A. P.: 'Radar detectability and collision risk, nautical briefing' (Nautical Institute, 1995), Tables 2 and 6 7 LANG, G.: 'IfGPS fails', Seaways, The InternationalJournal of the Nautical Institute, 2002, reporting a Royal Institute of Navigation Technical Committee Meeting of 26 June 2002 8 LATHAM, C. and STOBBS, A.: 'Radar, a wartime miracle' (Sutton Publishing, 1996) 9 COX, P: 'Memories of surface warning radar' Transmission Lines, The Newsletter of the Defence Electronics History Society, Bournemouth UK, 2003, 8 (4) 10 SOLLOSI, M.: 'The automatic identification system and vessel traffic services', IALA Bulletin, 2003,1, p. 20 11 MACLACHLAN, M.: 'The shipmaster's business companion' (The Nautical Institute, 2003, 4th edn.) 12 COCKCROFT, A. N. and LAMEIJER, J. N. F.:' A guide to the collision avoidance rules' (Stanford Maritime, London, 1976) 13 HALL, M. R M.: in HALL, M. R M., BARCLAY, L. W. and HEWITT, M. T. (Eds): 'Propagation of radio waves' (Peter Peregrinus for The IEE, 1996, 1st edn.), Preface and Chaper 1, Section 1.5 14 POPE, M. (of Sperry Marine): 'Marine radar technology. Current status and future directions', Seaways, the International Journal of the Nautical Institute, 2002, p. 11 15 BARTON, D. K.: 'Radar evaluation handbook' (Artech House, London) 16 KINGSLEY, S. P. and QUEGAN, S.: 'Understanding radar systems', (McGraw-Hill, New York, 1997), ISBN 0-07-707426-2 17 SKOLNIK, M. L: 'Introduction to radar systems' (McGraw-Hill, New York, 1983), ISBN 0-07-066572-9 18 BISHOP, O.: 'Understand electronics' (Newnes, Oxford, 2nd edn. 2001) 19 HAGEN, J. B.: 'Radio frequency electronics, circuits and applications' (Cambridge University Press, 1996)

Chapter 2

The system and the transmitter 'Power corrupts, but lack of power corrupts absolutely.' A Parody of Lord Acton

2.1

The operator and the system

2.1.1 Scope of chapter This chapter outlines radar operation in general terms, and then describes the transmission systems of the relatively large radars used in deep-sea ships, vessel traffic service (VTS) systems and firing-range surveillance. Receiving systems are described in Chapter 3. Chapter 4 onwards detail the various facets of the detection problem, including quantitative analysis. Figure 2.1 shows the whole radar/target/environment system. A person is studying the traffic situation at the display console. No mere passive observer, this officer adjusts the radar controls to optimise the display of targets of most current importance. Stressing this interaction, we refer to the person as the operator. The display itself, sometimes still called the indicator or scope, with associated controls forms the human-machine interface (HMI) between the radar and operator and one task of this book is to consider how the machine can best help the human perceive the targets apprehend them within the mind to gain situational awareness. Figure 2.2(a) shows a traditional deck-mounted console, while Figures 2.2(b) and (c) depict alternative formats suited to building into operator workstations.

2.1.2 Operators afloat Radars on merchant ships, including vessels subject to IMO's high speed craft (HSC) code, are primarily operated by the officer of the watch (OOW), who is the ship's master or a qualified deck officer. The radar(s) are one of the principal tools which aid navigation of the intended route, avoid collision with other craft and confirm positions determined by satellite and other means. The OOW may be the sole person

Radar

Environment Atmosphere

Precipitation

Scanner height H May roll, yaw or pitch

Feeder, if fitted Target height h may move

Transmitter/ receiver

Range, R Echoes, clutter and noise Processing and display Operator Sets controls Observes display, makes decisions

Figure 2.1

Sea surface Waves reflect unwanted clutter ^ Depend on Forward reflection at grazing point / wave height

The radar system. The operator controls the radar to best observe the target of interest within its environment. The system elements interact; all affect detectability. Radars and targets may be afloat or groundfast

on the bridge during daylight, but at night or in thick weather must be assisted by a seaman lookout, perhaps posted at the bow in telephone contact, but usually on the bridge, keeping visual and aural watch for ships and other hazards but never using the radar. HSC always have two navigators on duty. Figure 2.3 shows a typical bridge layout with displays and controls available to either officer's chair. A pilot with special local knowledge may be hired to advise the master and often conns the ship, using the radar as would the OOW. The Master or 0OW then monitors the proceedings, partly by observation of the radar secondary viewing display, but remains in charge. A seaman helmsman or quartermaster may actually steer the ship under orders, but never uses the radar. Pilots in some VTS systems are provided with portable laptop computers incorporating modems and radio links giving copies of the current VTS display for the local area, independent of the ship's radar, perhaps revealing targets masked from the ship by bends in the waterway, and annotated with VTS alpha-numeric data. It is less usual for shore radars to transmit data direct to the portables, dispensing with a VTS centre but providing all ships with a common overall high-quality view of the traffic situation. AIS radio-based systems such as the Tideland Signal AIMS Base are now available, offering radarless VTS, claiming all the precision, accuracy and reliability without the costs and maintenance. It will be interesting to see how well they catch on. Pilots and OOWs hold Certificates of Competency or 'tickets', awarded by a national authority. Radar operation and display interpretation are taught and examined prior to award, standards according with IMO's Convention on Standards of Training,

Figure 2.2

Deep-sea marine radar. BridgeMaster E Series. All reproduced by permission of Northrop Grumman Sperry Marine Ltd, New Maiden UK. (a) Traditional deck-mounted console. Controls immediately below display screen, transmitter and receiver in base cabinet. For standing operator, substantial bracing handles for heavy weather. Menu-drive controls below display, (b) Desk-top display for use seated or standing, (c) Flat panel display on RCCL cruise ship Brilliance of the Seas. Bow 3 and 9GHz scanners for berthing, main scanners above bridge, (d) Main navigation workstation. Radar and chart displays, with engine and steering controls to hand by navigator s chair, Brilliance of the Seas, (e) (overleaf) Bridge wing workstation, again with radar and chart displays, Brilliance of the Seas

Certification and Watchkeeping (STCW). Deck officers frequently transfer from ship to ship and may be presented with unfamiliar models of radar, so the IMO Marine Radar Performance Specification includes detailed requirements for uniformity of display depiction and of controls and their labelling. As well as gaming hands-on experience at sea, navigators are taught on full mission or radar simulators ashore at nautical colleges. Simulators can replicate numerous scenarios, exercising the most effective operation and interpretation of

Figure 2.2

Continued

Figure 2.3

High speed craft command workstations. Typical layout with displays and controls available to either officer s chair. As always, a clear view forward is essential. Reproduced by permission of Kelvin Hughes Ltd, Ilford, UK

the radar. Students sometimes emerge ashen-faced from close-quarter situations they hope never to encounter at sea. Complete ship's bridge simulators take the process further by inclusion of life-like and interactive views of the surroundings, with a full suite of navigational controls. Naval officers are trained and examined in navigation much as their merchant navy cousins. Although naval bridge teams are larger, warships often take civilian pilots in unfamiliar harbours. Skippers and mates of fishing vessels (FV) are often

part-owners, or at least share voyage profits. Time is money to them, and they make full use of radar on passage. FVs are unmanoeuvrable while fishing and careful watch is kept for collision risks from approaching shipping. Owners of private leisure craft are not usually required to carry radar or be trained in its use, but will want to get the best out of an expensive gadget they have chosen to buy out of their own pockets.

2.1.3 Integrated bridge systems Beside radar, operators gain situational awareness from the view from the window, radio traffic now including AIS, sound signals and maybe night vision equipment; VTS may include radio direction finders and closed circuit television. The importance of the radar display varies sharply between, say, night in thick weather and heavy traffic, and daytime in fair weather with little traffic, when the display may legitimately go almost unregarded. Formerly, the navigation aids on a ship's bridge were almost autonomous, with minimal interconnection. Links to the radar were confined to heading and speed feeds from the compass and log for the True Motion and North-Up display modes. The radar(s), compass, log and other instruments each had their own displays, positioned in a rather uncoordinated manner. Nowadays the trend is to provide each member of the bridge team with definite seated work-stations, each having economically designed controls and displays appropriate to the member's function, see Figures 2.2(d), (e) and 2.4(a)-(c). The screens may be capable of displaying some electronic chart and other data as well as the radar picture. The radar, less display, then forms a sub-system of an integrated bridge system (IBS), being sometimes termed a black box radar. The ship's voyage data recorder (VDR; bright orange, but sometimes called a black box nevertheless) is used for incident investigation and training purposes. Among much else, it is required by IMO to record all the information currently presented to the operator on the master display of one radar, including range rings, radar status data (e.g. range scale), navigation alarms, etc., but not gain and other control settings.

2.1.4 Operators ashore VTS may cover conflicting traffic flows in a navigationally difficult sea area. The traffic area of port VTS usually extends well to seaward of the harbour area. A small team of operators, sometimes called watchstanders, is led by a supervisor who may be the Harbourmaster. Methods of operation vary with port size, traffic patterns, local practice and the legal regime. There may be half a dozen sectors, each with its radar or radars, target data being handed from operator to operator as the ship transits the area. Beside radar, the operators use other sensors and information to build up situational awareness of the current and intended movements, anticipating conflictions and advising traffic to take appropriate actions; for example requesting or requiring a small vessel to keep clear of the deep channel while a supertanker passes. Except perhaps in extremis, for legal and other reasons VTS operators are not generally responsible for fine detail of movements or collision-avoidance manoeuvres - they

Speed Compass Depth Heading Azipod Indicators

Internal comms Monitoring systems

Multi-function display DGPS Engine controls VHF and internal communications CCTV

Figure 2.4

GMDSS Communications VHF HF SAT-C


Auto pilot Int. comms Engine controls Bow thruster VHF Steering wheel

Compass mon Chart table Nav. equipment Echo sounder

Radar ECDIS DP-CSS Monitoring Conning


Multi-function display DGPS Engine controls VHF and internal com munications CCTV

Liner RMS Queen Mary2, Cunard Line. A Il courtesy Kelvin Hughes Ltd, Ilford UK (a) The largest passenger ship afloat, 150 000 gt. Entered service between Southampton and New York 2004. The bridge occupies prime space, the top floor forward. (Artists impression.) (b) Bridge console contents. This comprehensive outfit omits to mention the allimportant Mark 1 Eyeball, (c) Main radar and pilotage consoles, shaded in(b)

do not seek to drive the ship. Training standards meet the need of the particular port. Some states have national standards, others do not, since individual VTS systems vary so widely in complexity. Internationally recognised unified training standards are however being introduced through IALA and IMO. A surveillance system with many similarities to VTS was mentioned and illustrated in Chapter 1, Section 1.2.5. There is a tendency to provide shore pilotage assistance from VTS centres, along the lines of Air Traffic Control. Only one aspect of this vexed question concerns us, registration of the targets displayed on the ship and shore radars, viewed by the 0OW and by the shore pilot, respectively. •

•

Instead of using the ship's radar to detect local targets, the VTS radar must display all of a group of distant targets in correct register to the piloted ship, demanding particularly high performance. A degree or so bearing error, trivial on the ship's display, might translate into a quite unacceptable relative positional error. Displays used by the shore pilot and the OOW should both contain exactly the same set of targets. Given a pair of weak targets A and B ahead of the piloted ship, there is rich possibility of confusion should the ship detect Abut not B, while the VTS, with its different aspect, detects B but not A.

Surveillance radars on coastal gunnery and missile firing ranges primarily ensure the hazard zone is clear of non-participating vessels, secondarily control movements of military craft participating in exercises. The civilian or military operators are trained and drilled in radar operation, interpretation and safety procedures. As members of the Range Safety Officer's team they operate to standing instructions which stress safety to all. Modern ranges take safety seriously. A UK Ordnance Board officer once told the author that they classed as a 'frequent occurrence' a life-threatening hazard predicted to arise once per 10 000 years. On the other hand, one has heard of a tanker master finding a deep indentation in the deck plating after passing a certain Mediterranean rocket range. Fixed or mobile surveillance radars, often adapted ships' radars, are increasingly employed by Coastguard or Police forces on anti-terrorist or drug interdiction missions, again after suitable training. Feeds may also be taken from VTS installations, where the security dimension is becoming an important factor in system design.

2.1.5 Basic radar operation Conventional marine and VTS radars generate a steady train of pulses - bursts of oscillation - of microwave power. An antenna transmits the energy in a continuously rotating beam as shown in Figures 2.5(a) and (b). Any object in its path scatters the radiation reaching it. A very little returns to the radar. Object bearing is that of the antenna, range being measured by the delay before reception. Let us look at the process in a little more detail, giving some typical shipborne radar performance parameters - like many of those quoted later on, these are approximate and vary from radar to radar. The pulses have quite high power of 1OkW but very

Pulse 1

Vertical Range, km

Transmission Max instrumented rang© Slope = velocity of light (300m/|ls)

Reference bearing (North or ship's head) Scanner location

Pulse 2

Target bearing Echo 300m/ns

Target range

Rotating fan beam After max range of pulse 1

Reflecting target (a) Perspective view

(c) Ranging

Reference bearing

Time, jus

Elapsed time measures range

Bearing as scanner

Scanner location

Own radar

Predicted position at time of scan 10..

Scale range proportional to echo delay

Half a dozen sweeps per scan

(b) Plan

Figure 2.5

Successive target positions Scan 4 (current scan) form echo trail Scan 3 (memorised) Scan 2 (d) Track on ppi display Scanl

Radiolocation and ranging

short duration, 1 |xs or less. A pulse is transmitted at the speed of light, 300m/|xs, sweeps out and strikes any scatterer on or above the sea surface lying in its path, indicated by the direct path of Figure 2.1. Some of the incident energy is absorbed within the scatterer. The remainder is scattered through a broad solid angle. The tiny part returning to the antenna forms an echo. Knowing that transmission and echo each propagate at the speed of light, the elapsed time to reception measures echo range, Figure 2.5(c), with uncertainty inversely proportional to the pulselength. The two-way scaling is 150 m/|xs or 6.67 |xs/km. In radar work, time and range are often interchangeable. Each transmitter pulse is in effect 'time stamped' for measurement of echo delay. After waiting long enough to receive the echo from a possible scatterer at the longest range of interest, another pulse is transmitted, the time between successive transmissions being the sweep time or pulse repetition interval, typically 0.001 s or 1 ms. A steady train of such pulses is emitted, the pulse repetition frequency (prf) being 1/0.001 = 1000 pulses per second (pps); pps is preferred to Hz to stress the extremely non-sinusoidal waveform. Sometimes prf varies with control settings. A few ancillary displays may operate ambiguously, with two transmissions simultaneously in flight. The directional antenna radiating the pulses is called a scanner. Its beam rotates continuously at 25 rpm and typically covers 25° in elevation to cater for roll of the platform (ship carrying the radar), but is only 1° wide. Any particular scatterer is therefore scanned every 60/25 = 2.4 s for a period of 2.4/360 = 0.0067 s, being illuminated by a packet of 0.0067/0.001 = 6.67 successive sweeps, say half a dozen, Figure 2.5(Z)). Any echoes received during this period are assumed to come from objects lying on the known azimuth bearing currently being illuminated, azimuth accuracy approximating the beam width, Figure 2.5(d).

The positions of all detected objects in range and bearing (polar or R, 0 coordinates) are therefore determined on each scan. Their echoes are laid down to scale as plots on a display screen called a plan position indicator (ppi) which informs the operator of their positions relative to the radar. Plots are refreshed by the new measurements taken on each scan. By following the progress of a plot over several scans, the operator can determine the object's track or course made good relative to the radar. Historic plots may be shown as trails, roughly indicating target course and speed during the last few scans, Figure 2.5(d). Targets are all objects, such as ships, of current interest to the operator. Although the Collision Regulations are written round aspect (relative bearing of target centreline) as indicated visually by navigation lights, often the radar discrimination is too coarse separately to display the individual scatterers comprising the target object and thus its aspect. Heights cannot be determined by radar. Radar is valued for its ability to position targets in range as well as bearing, and its general independence of cooperative equipment at the target. Although good signal processing facilities do the donkey work in presenting the clearest possible display, only the operator can decide that vital question - what to do?

2.1.6 Target detectability Targets can only be displayed and tracked when the echo power or signal can be distinguished or detected with reasonable certainty from competing clutter, electrical noise, and such man-made interference as the transmissions of other radars. Figure 2.6 shows a ship's radar display with clearly visible coastal features. Areas of speckling over the sea surface are clutter caused by rain squalls and would mask any small target echoes within. We will now briefly examine these and other factors which affect detectability. They are discussed in detail later in this book. When examining its passage through the atmosphere, the transmitted beam is often regarded as a bundle of linear elements called rays. The atmosphere subjects the rays to loss or attenuation and to variable curvature in the vertical plane on both transmit and receive legs. Figure 2.1 indicates that there are both direct and indirect ray paths between scanner and target, the indirect path being formed by intermediate reflection at the sea surface. Interaction between the two rays causes constructive or destructive multipath interference. At long range, the horizon intrudes on the scanner-target path. Having reached the target, the proportion of unit incident transmitter power reflected back towards the radar governs the apparent reflecting strength of a target and is called its radar cross section (RCS, defined in Chapter 7, Section 7.1.1, and sometimes called cross section area, CSA). Most targets, such as ships and coastlines, are inanimate or passive. Racons, RTEs and SARTs (radar beacons, radar target enhancers or active reflectors; search and rescue transponders, Chapter 8) are active devices which include a reception and retransmission process. Although much modified by environmental effects, transmissions reaching any target basically follow an inverse square law and returning echoes or responses again follow this law, so echo

Figure2.6

Ship's basic radar display. Atlas 9GHz monochrome (green) raster cathode ray tude display, 12nmi range scale, North-Up. VRM set to 5.35 nmi, measuring range of a ship target bearing 228°. Own ship heading 177°. Rugged cliffs of Cape Wrath, NW Scotland, to South; the lighthouse is not conspicuous. Rain squalls to NW and SSE would mask small ship echoes. Two blind arcs astern (North) from masts. Alphanumeric data around edge of screen. Lighthouse tender Pharos. Author, reproduced by permission of Northern Lighthouse Board, 1997

power, S9 at the radar tends to follow an inverse fourth power law of range, R; (S ex \/R4, discussed in Chapter 4). Clutter arises from scatterers such as a volume of precipitation or an area of sea-waves, not interesting to the operator. Their returns clutter the display and so hinder perception of targets. Although we will often use signal loosely, properly speaking signals convey information, wanted or unwanted. Echoes are signals but transmitter pulses are not, for they contain no information. Each echo is tiny (10~6 to 10~12 W) and may fluctuate in strength, say as own ship or the target ship rolls. The signal to noise-plus-clutter ratio, often shortened to SNR, is of great importance. Unavoidable imperfections within the radar receiving system also generate clutterlike background power, called noise. Because noise and clutter are random in nature, detection is never clear cut. There is always some probability of detection (PD) less than unity, associated with a finite probability of false alarm (PpA)- AS to be expected from information theory, high SNR raises PD for any given PFAFor detection on a single sweep with acceptably high PD (>0.5) and low PFA (< 10~6), echo amplitude must exceed the adjacent noise and clutter by a large margin (SNR at least 10:1 power ratio or 10 dB) - there must be adequate contrast. Candidate events are winnowed by thresholding, only returns above a predetermined strength passing to the signal processor following the receiver, where they are assigned to the appropriate one of an array of detection cells or bins in range and bearing. Detection is improved by having several sweeps per beamwidth and averaging or integrating them. Echoes, being associated with a definite position, are statistically correlated and their counts build up more rapidly than those of clutter, noise and interference, which are more random in nature and decorrelated. Targets are declared valid when there is

Figure 2.7

Display with radar, ARPA and ECDIS data. Flat panel eleven-colour display. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK

more than a certain number of counts, blips or hits per scan on which SNR exceeds a threshold value. Additionally, sometimes returns are required to meet detection criteria on two, occasionally more, successive scans, called scan to scan correlation. The operator, helped by built-in circuits and software, selects appropriate radar settings to optimise, as far as possible, echoes rather than clutter on the display; that is, seeks to optimise displayed SNR. Maximising SNR is the key to many aspects of radar design and performance, preserving the information within echoes while keeping noise and clutter down to acceptable limits. Current target positions are displayed as plots, points of light, generally on a raster display, formed from the raw polar data by a digital scan converter (DSC). The process of joining sequential plots by a line to display a target track or vector is called track-forming. Ancillary devices called automatic radar plotting aids (ARPA) or automatic tracking aids (ATA) automate this process and can generate numerous tracks unless overloaded when an excessive number of clutter returns arising from low SNR give high PFA- Plotting aids can extrapolate tracks to estimate future target positions, closest point of approach to own radar (CPA), time of CPA (TCPA) and can activate alarms should a target enter a guard zone around own ship. Accurate prediction demands high SNR (Chapter 13). VTS radars operate similarly and often include more elaborate forms of ARPA. They may combine data from several radar heads or from other sensors, particularly electronic charts; Figure 2.7. This data fusion, although technically difficult, can refine display quality and improve SNR. Marine radars will soon be required to associate radar plots with AIS reports.

2.1.7 Radar construction The plethora of 50 valves (vacuum tubes), resistors, capacitors and inductors of early radars has given way to in excess of 50 integrated circuits but few other components. Each IC has an area of a couple of square centimetres and contains many - sometimes many thousand - transistor elements, each functionally equivalent to a valve. The

ICs draw some 10 mA apiece, at the low voltage of 5 V. They are assembled on a few multilayer printed circuit boards and there is muck less bulk. Cable bundles are few. Digital technology predominates, and computers are also widely used during design. Extensive climatic and durability tests are performed at extremes of temperature, humidity, supply voltage, vibration and mechanical shock, especially on the scanner and upmast transceivers which inhabit an extreme (Class X) environment. These developments have transformed reliability, greatly enhance performance and have reduced price. Instead of renewal of a failed component, repair is generally by change of a complete sub-unit such as a board. Service engineers no longer need to know the minutiae of circuit arrangements, so manufacturers no longer divulge physical or software design details in service manuals. By jealously guarding their intellectual property rights much more than formerly, they make it well-nigh impossible for an outsider to infer the detection strategies used in specific models, or to describe in detail how they detect their targets. Use of proprietary application specific integrated circuits (ASICs) further obscures detail of operation. But even the subtlest designs must obey the laws of physics, enabling us to clearly state the boundaries of available performance, which we can be pretty sure all modern radars closely approach. Descriptions here and in later chapters are therefore to be regarded as basic concepts, intended to show in broad terms how and why transmissions are generated, reach targets, reflect as echoes, are detected and are displayed to the operator.

2.1.8 Decibels Radar calculations often involve outlandishly large or small quantities - we have already encountered transmitter power 10000 W and received echoes of IpW (10" 12 W). It is often convenient to express such quantities logarithmically, using decibels to give handier values which are added and subtracted rather than multiplied or divided. The dictionary1 definition cannot be bettered: Decibel: A logarithmic unit (one-tenth of a bel, abbreviation dB) used to express the ratio between two levels of sound intensity, electrical power, etc, one of which is usually a (stated or unstated) reference level...

Power ratio in decibels, P^B? of power Pi (watts) relative to power Pi (watts) is defined as: PdB = I O l O g 1 0 ^ .

(2.1a)

From this, ^- = I O ^ / 1 0 .

(2.1b)

Note that decibels are power ratios. Power itself may be expressed as dBW or dBm, meaning dB relative to 1W or to 1 mW (we use dBW exclusively); RCS as dBm2, 1

Shorter Oxford English Dictionary.

-infinity dB at 0

Power ratio or Power, watts

Figure 2.8 Decibels. Relates power ratio to dB and power to dBW. Scaling can be extended indefinitely using fresh pairs of axes as shown, the curve always remaining the same shape. Any 2:1 change in power is always a 3dB change, a 10:1 change being 1OdB dB relative to Im 2 , sometimes written dBsm or dbsm. Unlike some authors, we do not express distance in dB form (dB relative to 1 m). Time is never expressed in dB and millibels, kilobels, etc., are never used. To add powers which are expressed in dBW, they must first be converted to watts by Eq. (2.1b). Figure 2.8 plots the earlier expressions. Where voltages are denoted V and resistances R, and remembering that P a V 2 , substitution into Eq. (2.1a) gives PdB = IOlOg U ^ I dB. Lv2 //?2 j

(2.1c)

If R\ = /?2 but not otherwise PdB = IOlOg(ÛdB

(2.Id)

PdB = 20log ( ^ d B .

(2.Ie)

or

Logarithms cannot be taken of negative numbers so Eq. (2.Id) is more general than Eq. (2.Ie). For d.c. or a.c. phasor quantities V\ and Vi are the magnitudes (always

positive) of the voltages across the (equal) resistances R\ and R2. Corresponding forms are used for currents. Decibel conversion is straightforward using Figure 2.8, a PC or pocket scientific calculator's 'Log' and' 10 A ' functions. Tens of dB multiply by 10,100... etc. Negative dBs can be split thus for calculation: -127.3 dBW = -120 - 7.3 dBW = 1/1012 x 1/5.370 W = 0.1862 x 10" 12 W. Examples: OdB = 1 : 1 , I d B - 1.26 : 1, 0.1 dB - 1.023 : 1, - 3 d B ~ 0.5 = 0.5 : 1, 5dB ~ 3.18 : 1, 1OdBm2 = 10m 2 , 3OdB = 1000 : 1, -123 dBW ~ 0.5xlO~ 12 W; 0 dBm = 1 mW = - 3 0 dBW; 0 W(zero power) = —oc dB, emphatically not 0 dB.

2.2

Components of the radar

The following description concentrates on big-ship radars, which lie between the large VTS sets and small-craft radars.

2.2.1 Transmission Each transmitted pulse is a pulselength burst of sinusoid having the very high frequency necessary for efficient propagation close to the sea surface, typically 3 or 9.4GHz (3 or 9.4 x 10 9 Hz). Corresponding wavelength is 10 or 3.2 cm, much shorter than conventional radio practice. The radar is therefore said to operate at microwave frequency or centimetric wavelength. The microwave sinusoid is the carrier (or bearer) of frequency / c , modulated by a train of rectangular unidirectional baseband or video pulses, shaped as Figure 2.9(a), at the prf frequency / m , typically 1 kHz. The microwave magnetron power oscillator is switched on for the duration of each pulse by a modulator device. Modulation superimposes the train on the carrier; Figure 2.9(b). Speaking generally, although the energy of a sine wave signal is concentrated at a single (fundamental) frequency, all pulse trains have energy components spread between the fundamental (the prf) and its harmonics. A pulse train, prf = / = I/T, having pulses of any desired shape, can be synthesised by summation of a judiciously chosen d.c. component, plus a Fourier series of sine waves of frequencies / , 2 / , 3 / , . . . , nf, of appropriate amplitudes and phasing. (It is permissible to speak of phasing of these differing frequency components because they are harmonically related.) Where the ratio of the pulse on time, r, to the pulse repetition interval is k = r/T9 the frequency of the nth harmonic, / n , is

fn=nf=n-

n

=

±.

(2.2a)

As the radar modulation is a pulse train rather than a sinusoid, / m is a spectrum of prf harmonics centred on / c , Figure 2.10, with two equal and opposite sidebands at frequencies (Zc+ /m)

and

(/c-/m).

(2.2b)

(a) Baseband pulses Time domain (b) Pulses ofRF Time domain

Occupied bandwidth, rectangular pulses (c) Rectangular pulse at baseband Envelope as (a) Pow< T densi y

(d) Rectangular modulation on carrier Half energy in each sideband Short pulses occupy a wide spectrum Occupied bandwidth, rectangular pulses

Lower sid ?band Upper iideband Mirror image Copies baseband

Frequency Video (baseband) frequencies

Figure 2.9

Microwave frequencies

Echo spectrum. Infrequency domain, lower and upper sideband voltages are mirror images centred on carrier frequency / c

Each sideband contains half the pulse energy so occupied bandwidth is doubled to ±.0.5/x as shown in the transmitted spectrum envelope of Figure 2.9(d). Short pulses, especially those having sharp edges, of necessity occupy a wide spectrum. Energy density (watts per hertz) in the far skirt regions, although low, may be enough to interfere with users at other frequencies. Imperfections in the magnetron may introduce unwanted further spectral components. Occupied modulated bandwidth = - .

(2.2c)

The baseband spectrum of Figure 2.9(c) has bandwidth extending from zero to0.5/r. Occupied baseband bandwidth = — Hz.

(2.2d)

Conversion between time (Figures 2.9(a) and (b)) and frequency (Figures 2.9(c) and (d)) domains is possible using mathematical Fourier transforms. The harmonic voltages of a rectangular pulse of height £ R are given by an infinite series comprising a d.c. term JCER9 fundamental and harmonics. 2

i

V = &£R H—/SR Y^ - sin nnk cos nx,

n

(2.2e)

^ n n—\

where x = 2nT. Radar pulse trains have k so low (~0.001 max) that the d.c. term can be neglected. The amplitude of the nth harmonic, Vn (of frequency fn = nk/x Hz) is found by

(a) Block diagram Non-coherent system Self-oscillating magnetron High power pulses

Target

Scanner

Automatic frequency control

Free-running local oscillator

Low power trigger pulses Pulse generator

Demodulator T Video Signal Processing

Band pas; filter

noise Circulator or duplexer Low amplifier and receiver protection if used

Modulator

IF amplifier

Mixer

Receiver

Digital

Scanner bearing

Transmitter

Display

Timing

M, IF - Microwave, intermediate frequency (b) Time domain P. Modulator pulse

(as Figure 2.9(a))

Q. Magnetron output

(as Figure 2.9(b)) Time delay set by target range R. Receiver input

White noise

Noisy echo Repeats after ~1 ms S. Filter output

Bandwidth-limited noise

Edges affected by filter bandwidth T. Demodulator output Narrow filter bandwidth broadens pulse, causing range uncertainty Time, us

Range measurement

(c) Frequency domain - reception of echoes

White noise

Incoming echo (as Figure 2.9(d))

Local oscillator offset by IF frequency IF signal after mixer and bandpass filter Spectrum truncated to IF bandwidth

Baseband signal

after second detector

(d) Reception of image frequency

IF signal

Frequency, MHz

Image frequency signal sidebands reversed Frequency, MHz

Figure 2.10

Radar block diagram and signal flow. Time and frequency domains. Typical 9 (and 3) GHz band frequencies indicated. Block diagram (a) represents the usual non-coherent system

setting the cosine term to its maximum value of 1.0: Vn max = ——— sin(7r/ w r).

(2.2f)

Figure 2.10(a) is a block diagram of a typical radar, and depicts signals in time and frequency domains. The components are grouped within two or three physical modules. Low-power trigger pulses fire the magnetron via the modulator. The magnetron block has too much power abstracted from it (low 2-factor) to define magnetron frequency exactly. The magnetron output feeds the scanner. Echoes are routed to the receiver and thence to the demodulator, which removes the carrier, leaving a baseband or video pulse train similar to that generated by the pulse generator, but with delay proportional to target range and, at a given range, height (voltage) dependent on echo strength. The video train is processed to decide which pulses are likely to represent echoes rather than noise or clutter, then fed to the display for viewing by the operator. Figure 2.10(b) shows events during a single sweep. The pulse generator delivers a train of trigger pulses at prf near 1000 pps to suit the operator's choice of range scale. (A slight timing jitter to help suppress interference from other radars is not shown). The pulses fire the modulator, whose output, P, is a train of powerful (25 kW) pulses at the selected length. The magnetron is 40 per cent efficient and generates 1OkW (40 dBW) bursts of oscillation, Q, centred on the microwave frequency of its resonator in the 3 or 9 GHz bands. The pulsed nature of the transmission causes a fairly broad frequency spectrum to be radiated by the scanner.

2.2.2 Reception A circulator or duplexer (device routing bidirectional signals) directs the return signal R to the receiver, whose input circuit is preceded by devices to protect its sensitive components from burn-out by the powerful transmitter pulses. The first stage is usually a low noise amplifier working at microwave frequency, which lifts the echo voltage well above unwanted noise injected by later parts of the receiver. Microwave amplifiers are expensive and inconvenient, so the main amplification is done at a lower frequency called the intermediate frequency (IF, 50 MHz). Figure 2.10(c) shows the frequency relationships within conventional marine radars. The signal R is shifted bodily down to IF, here 50 MHz, at point S by a mixer, sometimes called a first demodulator or first detector, the receiver being a superhet (supersonic heterodyne). In more detail, when the weak microwave signal is superimposed with a strong sine wave from a continuously running local oscillator, LO, whose frequency is offset from transmitter frequency by the intended IF frequency; this oscillation beats with the echo. Components are generated at the sum and difference of the two frequencies, the latter being accepted as the IF. A symmetrical arrangement of diodes is used as a balanced mixer, which introduces no LO noise. Balanced mixers have a noise factor around 8 dB so receivers without LNAs have system noise factors around 9 dB.

2.2.3 Non-coherent system The LO in the system described is a free-running semiconductor microwave oscillator with output power of a few milliwatts. Its frequency must remain approximately tuned to any drifts in magnetron frequency otherwise the mixer output would drift out of the passband of filters further down the receiver. Tuning is primarily by an automatic frequency control (AFC) circuit which applies a correction voltage proportional to IF frequency error to the LO. The correction is typically derived from the changing phase of the double balanced mixer output. A manual fine tune control and associated tuning indicator are sometimes provided. Within AFC limits, LO frequency 'does its own thing' - it is not exactly harmonically related (is non-coherent) to transmitter frequency. In Figure 2.11 (a) the block diagram is redrawn to emphasise the frequency-determining elements, here shown for the 3 GHz band. While the modulator is firing, the magnetron output (Q) centre frequency is determined by the anode resonator block dimensions, surrounded by a spectrum based on that of the modulator pulse, P. The echo (R) spectrum is more or less identical (target RCS is only slightly frequency-sensitive), although of course echo power is drastically lower. Extra IF bandwidth has to be retained to cover the residual tuning error, degrading SNR, since noise power is proportional to bandwidth. On long-range scales, where receiver bandwidth is least, residual tuning errors may cause some loss of receiver sensitivity, further spoiling SNR. If the limited range of the AFC is exceeded, it may throw off to a large error, grossly degrading receiver performance, so the AFC loop must be reset when the magnetron or other component is renewed. After the LNA, the echo is multiplicatively mixed with the microwave continuouswave LO oscillation, which preserves the spectrum, shifting it bodily to IF. The echo is amplified in a multistage IF amplifier, containing bandpass filters. Filter centre frequency is the nominal difference between LO and magnetron frequencies and bandwidth has to be wide enough to accept the main components of the pulse spectrum, its occupied bandwidth. The IF output, S, is applied to a diode demodulator where it is rectified to give the baseband video pulse, T, whose spectrum approximates modulator pulse P, with amplitude proportional to echo strength at R. This envelope detection process preserves the envelope of the IF and microwave signals (compare Figure 2.10 S and T). The non-coherent system just described is wasteful of precious signal because the information resident within the echo phasing is discarded. The following systems improve SNR by preserving echo phase information but are more complicated. Use is currently confined to a few VTS systems.

2.2.4

Coherent-on-receive

system

Figure 2.\\{b) depicts one form of coherent-on-receive system, which seeks to retain the cost and efficiency advantages of the magnetron. The transmitter and receiver are basically as the non-coherent system except for the local oscillator,

(a) Non-coherent Restatement of Figure 2.10(a) with different emphasis AFC keeps LO near one IF away from Tx Automatic frequency control loop

Transmitter Power oscillator Frequency source Magnetron

Free-running

Frequency discrimination

Diode demodulator

Scanner

Duplexer

Power modulator spectrum = P

to signal processor

Protection

Mixer

Video Spectrum = P Phase information lost

IF amplifier

Centre frequency 50MHz

Bandwidth wide enough to cover LO frequency error

(b) Coherent-on-receive

Flywheel synchronisation

Locked to magnetron at each pulse

Transmitter Power oscillator Frequency source Magnetron

COHO 50.00MHz

Coupler

Clock Coherent demodulator

to signal processor

Power modulator snectrum = P

STALO

Mixer

In-phase (I) Video Quadrature (Q) IF amplifier Centre frequency 50 MHz Spectrum = P Bandwidth matched to pulse Phase information preserved within I and Q channels (c) Fully coherent Frequency source 50.00MHz

Frequency locked to COHO

Multiplier x 59

Transmitter

High supply power

Scanner

watts Transistor TWT or klystron _ or TWT

Clock to signal processor

50.00 ± P MHz (IF frequency)

STALO

Modulator spectrum = P

In-phase (I)

Quadrature (Q) Spectrum = P Phase information preserved

Centre frequency 50MHz Bandwidth matched to pulse

50.00 ± PMHz (IF frequency) Items to right of dashed line differ for active arrays

Figure 2.11 Frequency management strategies. Typical 3 GHz band frequencies. Most radars are non-coherent whose frequency is synthesised as follows. A coupler (a pair of parallel waveguides linked by small slots, or parallel stripline conductors) extracts a sample of the transmitter frequency actually generated, from which the pulse sidebands are then removed. The frequency of this sample is remembered between pulses by either a flywheel oscillator or digitally and is maintained exactly at magnetron frequency.

It is mixed with the output of a coherent oscillator (COHO) which runs at IF centre frequency to give a stable local oscillator (STALO) signal. The figure shows typical frequencies. After the LNA, the echo is mixed with the STALO to give a pulse spectrum centred on IF centre frequency; this feeds the IF amplifier. Filter bandwidth can be matched to the modulator pulselength without need of additional allowance for LO tuning error. The demodulator is a pair of mixers taking direct and 90° phaseshifted drives from the COHO to give in-phase and quadrature (I and Q) video outputs, preserving both the amplitude and phase information contained in the echo. Successful operation is critically dependent on accurate capture of magnetron frequency during the transmitter pulse, followed by drift-free memory during the relatively long interpulse reception phase. Relative to non-coherent operation, integration loss is roughly halved. 2.2.5 Fully coherent system Figure 2.11(c) depicts a fully coherent system. The COHO is the primary frequency source, multiplication (here by 59 and 60) synthesising the STALO and transmitter frequencies, respectively. The continuous-wave transmitter feed is modulated by the pulse at low power (facilitating precise pulse-shaping and control of transmitter spectrum), followed by a multistage power amplifier, which replaces the magnetron. The STALO frequency is positively locked one IF frequency away from echoes at all times. The remainder of the receiver follows the coherent-on-receive system. Amplifier-type transmitters are bulky, inefficient and expensive, but give operational flexibility. Although not shown, it is straightforward to stagger transmitter frequency from pulse to pulse to decorrelate sea clutter and hence improve detection for a given SNR; or to reduce transmitter power; for short-range operation, for example. The amplifier may contain a travelling wave tube (TWT) feeding a klystron amplifier tube. Both are high voltage thermionic valves. Coherent systems are particularly suited to active array scanners, not in current marine service, see Chapter 16. 2.2.6 Ambiguity; image frequency, prf constraints It is desirable to maximise the number of sweeps - minimising sweep time - taken into the detection process to maximise the effective SNR and get maximum probability of detection for the chosen false alarm rate. But if sweep time is less than the range delay of the furthest target returning a detectable echo, it becomes uncertain or ambiguous whether a plot is from a close target reflecting the last pulse transmitted, or from a more distant echo of an earlier transmission. Ambiguity can be resolved by severely jittering (staggering) the pri but signal to clutter ratio then tends to suffer. Operation at relatively low prf is universally preferred, the radar being non-ambiguous out to the maximum instrumented range of the display (on big ships often 96 nmi, 178 km, constraining maximum prf to 840 pps on long-range scales). On short-range scales higher prf can be used. Beside minimising risk of receiving second time around

echoes, relatively low prf is often retained to enable plotting aids to continue to track targets which are too distant for current display, ready for the operator to return to long-range operation; to permit a second display to show the distant scene while the primary display examines the short-range scenario, or to service guard zones. Low-power radars can utilise high prf without risking significant second-time around echoes from distant targets, except under conditions of anomalous propagation or anaprop, Chapter 5, Section 5.2.5. It is questionable whether the 96 nmi instrumented range frequently provided serves much purpose, only inland mountains being likely to rise above the radar horizon. The operator is sometimes provided with a long/short pulselength switch. Long pulse/narrow bandwidth reduces noise and improves detection of weak targets if clutter is slight; short pulse/wide bandwidth improves range resolution and illuminates less clutter around the target, improving clutter rejection and helping to depict target aspect. Figure 2.10(d) shows that, depending on detail design, the receiver may be responsive or open to a band of unwanted frequencies lying on the other side of LO frequency from the transmitter. Usually this image frequency band contains nothing synchronised with the transmitter and merely contributes some additional noise, which is included within the overall noise figure. Swept-frequency racons are sometimes received at image frequency, see Chapter 8. Modern receivers include double balanced mixers which reject image frequency.

2.2.7 Typical station configuration Figure 2.12 shows a typical radar station and its links with other bridge equipment, Figure 2.13 being a particularly futuristic realisation of the bridge components. A pair of transmitter/receivers, if in the same band, may be connected to a single scanner by a combining device called a diplexer (not duplexer), diplex operation being the simultaneous transmission/reception of two signal channels using a common component such as a scanner. In principle it is possible to combine or fuse the receiver output data streams before feeding a single display. The difficulties exceed the advantages on shipboard, although data fusion is occasionally used in VTS. The bigger ships are mandated by IMO to carry two radars, primarily for reliability. One set has to use the 9 GHz band. IMO encourage the other to be at 3 GHz, giving the operational advantages of each band. Good seamanship usually requires one of a pair of radars or displays to be kept on a long range scale for landfall verification and to give early warning of traffic movement, the other running on a shorter scale for collision avoidance. Here the installations have their own scanners, but either's receiver output may be switched to the other's display, and it is not always very obvious to the operator which band is active. A very few merchant ships voluntarily duplicate their equipment with typically two each of 3 and 9 GHz radars. Many roll-on roll-off (ro-ro) ferries and some other ships carry additional small, usually 9 GHz, radars low down forward and sometimes astern to assist berthing. Lack of omnidirectional azimuth coverage unsuits them to general navigation.

Scanner

Transmission Rotating joint

1OkW Steady pulse train lOOOpps Delay proportional to RANGE

Echo

Bearing data

Pulse packet each 2.4 s

Feeder Coax or waveguide

Peaks at scanner BEARING Locating the target

Duplexer Duplicated VTS radar Circulator Protection Fourth-port loadi

Pulse transmitter

Low noise amplifier Superhet receiver Synchronisation

Signal processor

Transceiver As Figures 2.10 and 2.11 Velocity data (Log and compass)

Main Display Raster scan PPI

Controls; operator influences detectability

Figure 2.12

ARPA or ATA

Automatic radar plotting aid or automatic tracking aid Tracks targets after detection

Buffered video

Integrated bridge system (IBS) Electronic chart display and information system (ECDIS) Voyage data recorder (VDR) Secondary viewing displays

Typical station configuration. Twin-radar installations usually use two scanners which usually remain functionally independent even when sharing a display. The display may contain otherfacilities, particularly when forming part of an integrated bridge system (IBS)

The remainder of this chapter details how radars illuminate targets. Reception is detailed in Chapter 3.

2.3

Transmitter

2.3.1 Overview The transmitter, sometimes abbreviated Tx, is usually built as a unit with the receiver, Rx, to form a transmit-receive unit, transceiver or Tx/Rx. If not aloft with the scanner, the transceiver is located below deck, either within a stand-alone cabinet or integrated within the display unit. The necessary transmission line or feeder to the scanner introduces loss, noise and reflection clutter.

Figure 2.13

A modern trend in bridge workstation design. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK

A steady train of powerful, short, pulses of electromagnetic energy is required. The train is sometimes said to be uncoded, for it carries no data. In radio terminology, the emission type is PON. Equipment limitations preclude generation of truly rectangular pulses - and they would have undesirably wide spectral width - but it is convenient for most purposes to think of them as rectangular or 'square'.

2.3.2 Magnetron power source Except in coherent systems, the generator is usually a cavity magnetron valve (tube). The magnetron has always been the cheapest and most efficient power generator and is a transit-time high power oscillator. Within a sealed envelope it contains a central cylindrical heated cathode, surrounded by pairs of anode poles connected to parallel inductor-capacitor (LC) tuned cavities, the inductor centre points being earthed. The high-vacuum working space between cathode and the anode system lies in the strong axial field of a permanent magnet, the tube/magnet assembly thus forming a packaged magnetron. Application of a negative pulse of about 1 OkV to the cathode makes it emit electrons. They are subject to crossed fields, radial electric and axial magnetic, and take spiral paths. Some electrons return to bombard the cathode, increasing its emission to several amperes, but most fly to the anode poles. When a random grouping of electrons causes Poles 1 to fall slightly below earth potential, the centre-tapped tuned circuit forces Poles 2 positive. Electrons hitting —ve Poles 1 deliver more energy than absorbed by those hitting +ve Poles 2, so the oscillation builds up. After a microwave half-cycle the tuned circuits swing the pole polarities to Poles 1 +ve, Poles 2 —ve. This instant is arranged to coincide with the transit time of the spinning beam to Poles 2, feeding more energy into the tuned circuits. There are usually four pole pairs and the electrons cluster into four spokes. Intervening C-shaped cavities form the tuned circuits of the cavity resonators within the copper anode block. Frequency is therefore determined during manufacture and is ordinarily not externally controllable. Frequencies lie within sub-bands, usually

30 MHz wide, often located near the centre of the IMO operating band. The outermost 15 MHz 'guard bands' are always avoided to minimise radiation of outband spectral components. The power is coupled out by a short coaxial line launching into an integral waveguide. Magnetrons are simple and have long life, and have stood the test of time. Their remarkable efficiency makes for cool running and high reliability. Permissible duty cycle or on/off ratio is low and despite the high peak power, mean output power is only around 1OW (and waste heat needing to be dissipated is not much more), similar to that of shipborne very high frequency (VHF) radio with its quite different modulated continuous wave transmission. Actual transmitted pulse shapes are not generally disclosed by radar suppliers. Because target detectability is improved when there are many pulses within the packet, occasionally prf is raised so far on short-range scales that, to keep within the magnetron's maximum permissible duty cycle, pulselength has to be reduced below that essential for good range resolution. The scanner is never perfectly matched. When the feeder is long, quite minor frequency change sharply changes the phase of the mismatch power returned to the magnetron. To minimise risk of provoking unwanted 'long line effect' modes of oscillation (Section 2.6.1), with their poor spectra and low efficiency, usually either a ferrite circulator is used as duplexer (Chapter 3, Section 3.2.3) or a ferrite isolator (a non-reciprocal device; ordinary reciprocal devices and components behave equally to either direction of energy flow) is inserted at the magnetron output to improve load match. Similarly, the rate of rise of drive voltage has to be controlled. More expensive coaxial magnetrons have tighter spectrum control and are better suited to coherent systems.

2.3.3 Modulator The magnetron is driven from a modulator, designed to introduce insignificant noise. Typically the modulator contains inductors and capacitors in a pulse-forming network (PFN) - or formerly a coaxial cable containing distributed inductance and capacitance - which accumulates low-voltage energy between pulses. When a solid-state thyristor, silicon controlled rectifier (SCR) or high voltage insulated gate field-effect transistor (FET) switch is fired by a small trigger pulse, the PFN rapidly discharges in a controlled manner through a step-up transformer, whose high voltage secondary is bifilar wound to carry the magnetron heater current. In some designs, the inductors and capacitors in the line overswing to double voltage. Pulse length is changed by switching inductor/capacitor combinations. Widely varying lengths pose difficult design problems and a delightfully named tail biter diode is often used to suppress secondary short pulses; alternatively FET switches terminate the pulse in a more definite manner. Formerly modulators used hard-vacuum triodes, or thyratron valves containing gas at low pressure - the author's first radar task was production test of hydrogen thyratrons. Occasionally saturable reactors (pulsactors, Melville lines) were employed, where a control current pulse switched magnetically stored energy. These were heavy, complex and best avoided!

2.3.4 Influence of transmitter on system The modulator/magnetron arrangement of non-coherent transmitters constrains many characteristics of the whole radar. • •

•

• •

• • •

Only a few discrete pulselengths are available, modulator design constraints precluding smooth variation. Magnetrons are bang-bang devices. Transmitter power is either full or zero. Unlike radio, there can be no low-power mode, although peak power may be a couple of decibels less than nominal on the shortest pulselength. Power builds up very rapidly (^ 10 ns) at the start of the pulse and pulse-end decay is nearly as fast, broadening the frequency spectrum and necessitating output filters to minimise interference to other spectrum users. Transmitter frequency is built into the magnetron cavity and cannot be adjusted by the operator or service engineer. Frequency changes by 10 MHz or so due to heating, pulling (load match change, VSWR preferably being held below 1.3), pushing (drive voltage change) and ageing. The receiver has to match drift using automatic frequency control (AFC) or manual retuning and bandwidth has to include a margin for error, letting through more noise and effectively reducing receiver sensitivity and SNR. Maximum duty or pulselength/prf combination is dictated by prf to prevent overload. The cathode may take several minutes to heat from cold, necessitating a heater-on hot-standby mode. Small size and high efficiency permit compact installation, enabling mounting at the scanner, obviating wasteful feeders.

2.3.5

Spectrum

problems

It is difficult to tame magnetron output pulse edges and the output spectrum is undesirably rich in harmonics, often being especially dirty on short pulses. The anode tuned circuit is tightly coupled to the output to extract maximum power. Selectivity is perforce low, like a muffled bell, so the tuned circuit cannot fully suppress out-ofband frequency components. Other oscillation mechanisms become significant when the valve ages, especially when rate of rise of drive voltage is outside specification, and tend to cause spectral lines some tens of megahertz from centre frequency, called moding. Oscillation amplitude is limited by onset of saturation and cut-off effects which cause harmonics of the microwave carrier frequency to be generated. A rounded Gaussian pulse (shape similar to Chapter 3, Figure 3.5) would deliver a cleaner spectrum, lying almost wholly within the marine band, but magnetrons are unsuited to this pulse shape. Successful modulator design demands particularly close liaison with the magnetron supplier. At first the microwave spectrum was not intensively used. There were a few industrial and, later, domestic microwave heaters at 2.45 GHz and some low power industrial activities at 10.688GHz. Astronomical research receivers near 10 GHz demanded quiet conditions. Otherwise the civil and military radar fraternities had

the field to themselves. Although radar receivers are sensitive, the highly directional antennas invariably employed mitigate mutual interference. Civil marine sets employ prf stagger to break up 'running rabbit' interference - patterns of dots slowly traversing the display - from other sets employing similar frequency and mean prf. The military have to be prepared to counter hostile jamming, so can generally put up with considerable inadvertent interference. The situation had similarities to the spark transmitter days of early marine radio telegraphy. For many years there was therefore little objection to transmission of rectangular pulses, with their profligate spectrum. Rectangular pulses are particularly convenient to generate by discharge of a delay line into the transmitter valve, and facilitate good range resolution. As pointed out by Williams [1], the 1990s telecommunications explosion placed intense pressure on the lower microwave frequencies. Governments recognised the spectrum as a finite and valuable resource, to be auctioned to the highest bidder for billions of pounds. Covetous eyes focused on the centimetric bands. It is likely that radar will soon have to share the frequency bands with telecomms. While a good case can be made on safety and commercial grounds for pulse marine radar, together with sufficient spectrum for accurate range determination, it is hard to justify the pollution of adjacent frequencies by unnecessary transmission of rectangular pulses, not to mention moding lines and harmonics. Occupied bandwidth must be minimised. To a telecommunications receiver, it is peak power that matters, in other words the equivalent isotropic radiated power (EIRP), the power in the beam, the product of transmitter power and antenna gain (their sum when using dB). Radio circles prefer the term peak emitted power, PEP, which assumes radiation from a dipole of gain 2.15 dBi. Typical big-ship radars of say 2OkW peak power and scanner gain 1000-2000 (30-33 dBi) have very high EIRP, - 3 0 M W (75 dBW). As receiver noise in telecomm receivers is only a few decibels above the thermal noise floor of —204 dBW/Hz, they may encounter severe interference. Since 2003, Appendix S3 of the ITU-R Radio Regulations2 in essence requires out of band shipborne radar emissions to be 6OdB below EIRP, for example, 30 W in the example, the 'relative' phrasing of the regulation (inserted at military behest) giving little incentive to reduce EIRP itself. VTS radars are required to be considerably better. This situation is likely to be tightened within a few years; current relative friendliness to high EIRP may be rebased to require out of band emissions less than some specified 'absolute' low number of watts per megahertz. Some future spectrum control possibilities are outlined in Chapter 16. Currently, control is often by a bandpass filter at the magnetron output. Problems include space availability, designing to handle the peak power, provision of sufficient attenuation through to harmonic frequencies, energy loss in the passband and maintenance of good impedance match. If the filter appears highly reactive away from centre frequency, it may pull the magnetron frequency or provoke moding. Filtering has

2

ITU-R SM 329-7; Category A, Shipborne radar; Category B, VTS radar.

little practical effect on the shape, bandwidth or detectability of the received echo apart from introduction of ~1 dB insertion loss. Radiated spectrum depends on several linked features. • • • •

• •

2.4

Modulator detailed design, particularly the slope (MOOV/ns) and dynamic impedance of its output pulse. Magnetron detailed design. New 'third generation' designs being developed claim sharply reduced out-of-band spectral components. Magnetron age. Spectrum deteriorates near end of life. In-band load mismatch presented by the duplexer or output filter. Four-port circulators with matched loads (Figure 2.11 and Chapter 3, Section 3.2) are superior to three-port types. Out-of-band load mismatch. It is difficult to design filters to retain good match in the stop bands. The out-of-band scanner efficiency. If poor, out-of-band radiation is reduced.

Transmitted frequency

2.4.1 Frequency and wavelength Wavelength, X, is tied to frequency, / , by the velocity of propagation, c, which is the speed of light 299.7 x 106 m/s, conveniently remembered as approximately 300 m/|xs or 1 ft/ns. When the refractive index of the medium is n (1.0 for vacuum, ~ 1 for air) 299.7 x IQ6 A~

m.

(2.3)

Jn When it is necessary to confirm wavelength is in free space rather than some other dielectric, X is replaced by Xo. A frequency of 3.0 GHz (3 x 109 Hz) has wavelength XQ = 0.0999 m, ~ 10 cm. Operational frequency or wavelength can be indicated in various ways and fashions have changed over the years. • All marine and VTS radars are microwave (defined by wavelength 6 dB on axis.

Reflections from obstructions can also cause false echoes, see Chapter 10, Section 10.12.6.

2.7.10 Sidelobes Figure 2.20(a) shows that away from boresight there are cuts such as VW where positive and negative wavelets are equal and cancel, with no resultant energy, giving

nulls at bearings normal to the cut. The first nulls are OR and OR'. As the angle from boresight increases, the energy falls to zero at the first null, partially recovers to give the principal or first sidelobe, followed by further sidelobe nulls and smaller peaks. Although the mechanism differs in detail, reflectors and all other directional antennas also have sidelobes - indeed it is theoretically impossible to avoid them entirely. The outer parts of reflectors have to be illuminated weakly to reduce spillover and sidelobes induced by edge currents. Alas, beamwidths increase and gain falls. Scanners are precision devices and good sidelobe performance depends critically on element coupling and the straightness of the structure. Within limits, the designer can trade sidelobe strength against gain on axis. Many alternative aperture weighting strategies exist, the subject being something of a mathematicians' delight, see, for example, Meikle [5]. Often the illumination function has a variant of the 'cosine on a pedestal' form; Figure 2.18(c): relative voltage density at angle v from boresight oc 1 — (1 — k) cos(7rv) where k is a constant. The radar can only assume that echoes come from an object on boresight. Azimuth sidelobes therefore give false echoes. The art and science of scanner design is to minimise these sidelobes, by careful computation, illumination taper and precision slot-cutting. Principal sidelobes on big-ship scanners are at least ~23 dB below main beam, see Table 2.3 C, D. The higher sidelobes generally diminish by another 10 dB. Good scanner sidelobe performance can be ruined by close obstructions which deflect energy to unwanted bearings, causing sidelobe interference. Figure 2.23(a) illustrates a scanner having uniform elevation illumination, 25° beamwidth and heeled 10° by roll or pitch. Even under this adverse condition the first null strikes the surface at only three times scanner height, H9 with the second null at about 0.6H. One hopes targets will have been detected and any collision avoidance manoeuvre completed at much longer range. Null ranges are very sensitive to roll and pitch angle, so all targets are likely to be illuminated from time to time and elevation nulls are not usually too troublesome to ships' radar. Elevation sidelobes illuminate extra sea or precipitation clutter and waste expensive transmitter power.

2.7.11

VTS reflector scanners

Many VTS stations use slotted arrays; either standard marine types or derivatives having wider aperture, somewhat narrower elevation beamwidth and sometimes with choice of polarisation. When more gain or narrower azimuth beamwidth is required, e.g. for distant detection of approaching shipping or to monitor movements of possibly illicit small craft, although patch arrays are being introduced (Figure 2.22, Section 2.7.8), reflector scanners are generally used, Figure 2.24. As also indicated in Figure 2.25(a), a small primary radiator (sometimes confusingly called the feed) is mounted in front of the reflector. It may use a plain or corrugated horn or short vertical slotted waveguide, broad-face slots giving horizontal polarisation. The radiator is protected by a window and placed at the focus O of an open reflecting metal dish reflector shaped as part of a shallow paraboloid (parabolic in both planes) having focal

Boresight heeled+ 10° (boresight horizontal on even keel)

Scanner at 50 m

- 3 dB point, -2.5° To surface at 1.15 km First null-18.25°, 150 m Second null ~ -58° ~ 31 m Null ranges change with heel angle (a) Ship, fan beam

Elevation beamwidth 25°, heeled 10°

Scanner at 100 m

Boresight depressed 1° to meet horizon

- 3 dB point, -3° To surface at 1908 m

3rd null,-14.6°, 385 m Echo fluctuates with range, zero in nulls (b) VTS, fan beam Groundfast, elevation beamwidth 4°, depressed 1° Boresight

Cosec2 limit, -11 °, 515 m (c) VTS, inverse cosec2 beam

Otherwise as B

- 3 dB point, -3° To surface at 1908 m

Cosec2 scanner obviates nulls Echo independent of range until Earth curvature becomes significant at long range

Figure 2.23

Short-range cover. Shows position of scanner elevation events for: (a) Ship with high scanner: despite adverse heel, broad (20°-25°) elevation beamwidth covers surface to short range, (b) VTS with high scanner, 4° beamwidth, fan beam, troublesome nulls, (c) Inverse cosec2 beam obviates nulls

Figure 2.24

Dual-band coastal surveillance reflector scanner: 3 and 9 GHz bands, 36 and 44dBi gains. Bulky feed assembly contains polariserfor linear and circular operation. For exceptionally arduous operation at the Bay ofFundy, N Atlantic coast of Canada. Heater to prevent icing. Note the very stiff girderwork necessary to retain rigidity and microwave performance in high winds. Reproduced by permission of Easat Antennas Ltd, Stoke on Trent UK

Paraboloidal dish reflector

Spillover

Part of paraboloid Azimuth beam edge

Directrix Phase front Elevation aperture, b

Elevation beam

Axis No squint Primary radiator, e.g. horn

Horn

Offset feed at focus

Polarised

Focus

Path lengths OYZ, OY'Z' equal Control signal Rays all parallel to axis irrespective of frequency Plane wave from rotating joint and apparently originate at directrix Plan (a) Reflector

Figure 2.25

Azimuth beam edge Edge effects

Side elevation on DO (b) Offset feed

Reflector scanner. No azimuth squint. Offset feed avoids aperture blocking

length OP. Paraboloids have the property that all rays from the focus, after reflection at the surface, are (a) parallel and (b) have the same path length to the mouth, giving a plane-fronted pencil beam, very narrow in azimuth and narrow in elevation. The geometry is equivalent to radiation from the directrix one focal length behind the dish (PD = OP). The primary radiator is usually offset below the dish (Figure 2.25(b)) to keep it out of the beam. Blocking would spoil the pattern, introducing blocking loss. The blocking 'hole' in the illumination would act as a small negative illuminator, generating sidelobes at its edges. Reflector scanners have no azimuth differential squint and if designed for wide bandwidth, differential elevation-plane squint is minimal. The field strength contours are elliptical and the dish is made elliptical also; corners of a rectangular dish would be too weakly illuminated to pull their weight. Beamwidth is increased and gain reduced for a given aperture - power taken from the sidelobes in effect broadens the beam, reducing the aperture efficiency. Reflector scanners, beside having sidelobes near the boresight, suffer from spillover radiation, some energy from the feed missing the dish and forming far-out 'sidelobes' at around ±120° off axis. It is usual to minimise elevation radiation above boresight, which does not intercept the target and collects unwanted precipitation clutter in receive mode. Below boresight, the near-in sidelobes are often fused or integrated with the main beam to minimise loss of gain at sidelobe null angles, as with the inverse cosec2 type described shortly. Although some radio telescopes of great precision have reflector areas up to about 5000 m 2 , the economic limit for VTS is much smaller; around6mx 1 m aperture in the 3 and 9 GHz bands, and maybe two-thirds these dimensions at 14 GHz. Beamwidths

Table 2 A

Fan beam scanner elevation features

Illumination feature

^ power beamwidth 3 dB points 1st null lstsidelobe 2nd null 2ndsidelobe

Uniform v 0 0.50 1.2880 1.580 2.220 2.770

w

g(dB)

0.886 ±0.443 1.0 1.42 1.97 2.45

3 3 inf 13.3 inf 17.8

Cosine v 0 0.50 1.270 1.590 2.110 2.450

w

g(dB)

1.184 ±0.592 1.5 1.9 2.5 2.9

3 3 inf 23 inf 31

go down to about 0.35° azimuth at 9GHz, gain exceeding 43 dB. Illumination is always tapered to minimise azimuth sidelobes, at cost of a bigger dish for given gain and beamwidth. Computer design techniques such as finite element analysis, coupled with the additional data derived from near-field testing, enable modern reflector scanners to deliver considerably higher gain than previously possible, with lower sidelobes. All parts of the beam are fed in parallel, so very short pulselengths may be used. Designs are also less frequency dependent, facilitating improvement of performance by frequency diversity, described in Chapter 12, Section 12.8.

2.7.12 Elevation performance; inverse cosecant squared reflectors VTS elevation half-power beamwidths, 0, are about 10°-20° (slotted arrays) and 4° (reflectors). When mounted high, the boresight is generally depressed a degree or so to improve illumination of the horizon. Table 2.4 compares theoretical elevation performance for uniform and cosineweighted illumination models. The angles are almost identical for all sidelobe events and of course are somewhat dependent on wavelength variations across the frequency band. Performance of practical scanners is rarely published in detail, but is probably intermediate between these models. Beamwidth w links the featured angle with the wavelength/aperture ratio, thus, for example, j power beamwidth = wk/a, where factor w — 0.886 for uniform illumination or 1.184 for cosine illumination. As an aside, this indicates aperture of a cosine-illuminated scanner has to be 1.184/0.886 = 1.336 that of a uniformly illuminated scanner of the same beamwidth, the price paid for improved sidelobe performance. At the featured angle, gain is g dB below gain on axis. Alternatively, either the vertical curvature of the reflector may be made nonparabolic, or the feed radiation may be tailored, so that below the lower half-power point the pattern follows a nominally inverse cosecant squared pattern down to about — 10°, 'inverse' because the cosec2 law applies for angles of depression rather than

elevation as in air traffic control service. Echo strengths of surface targets then remain constant as range changes, particularly when the scanner is high and range fairly short, reducing the dynamic range demanded of the receiver. Figure 2.23(b) shows the nulls of a conventional VTS fan-beam scanner of elevation aperture 4° and depressed 1°. The first null lies at about 11//, about 1.1 km when H = 100 m. Changing to an inverse cosec2 type, Figure 2.23(c), eliminates nulls down to very short range. More energy is transmitted away from beam axis so cosec2scanners sacrifice a couple of decibels boresight gain on fan beam types of the same aperture. Choice of most cost-effective scanner for a specific application is not always clear-cut.

2.7.13 Polarisation The voltages at the edges of near-vertical slots in the narrow face of a horizontal slotted array generate H fields in elevation and E fields in the azimuth plane, so the radiation, mutually perpendicular to both planes, is horizontally polarised (HP); Figure 2.12(a). IMO requires all marine 9 GHz radars to have HP to give compatibility with racons and SARTs, which use this polarisation. A few 3 GHz band sets (Sperry Radar, cl970) preferred vertical polarization (VP), Figure 2.14(b), where the field planes are interchanged, the guide broad face being slotted as Figure 2.18(b). Here slot coupling is a function of offset from centreline. These slots are usually resonant, approximately Ag/2 long. Although marketed for marine radars at one time, circular polarisation (CP) facilities seem now to be confined to VTS. HP picks up least sea clutter from the regular waves typical of open waters but VP is better in coastal areas where seas are more confused. Circular polarisation, consisting as it does of equal HP and VP components, has intermediate sea clutter performance but is much better against rain clutter because the near-spherical shape of raindrops causes them to reflect at the opposite hand, which is rejected by the scanner in receive mode. At one time, CP was provided by dropping a grid of slanted wires over the primary radiator, but it is now usual to insert a waveguide network immediately behind the feed horn; Figure 2.24 (Section 2.7.11) shows the bulk of such networks. A waveguide switch selects HP or VP via plane-rotating elements. For CP, a second switch passes half the power through each rotator, with ±45° phase shift. Williams [6] has found that many targets depolarise echoes sufficiently for a cross-polarised receive mode to enhance echo to clutter ratio. An antenna transmitting say HP and receiving VP is designated HV mode, the ordinary mode being HH. Polarisers add complexity and some additional loss. Plane polarisation is used in clear conditions, because CP reduces RCS of many targets such as ships by several decibels. On reception, only the transmitted hand of polarisation is accepted. Echoes from scatterers having an odd number of internal reflections, for example, from a sheet or trihedral, as well as raindrops, come back with the other hand and are rejected. The measure of circularity is ellipticity = 20 log (ratio of outputs in the planes of maximum and minimum gain), dB.

(2.8a)

For wrong-hand echoes, for example spherical raindrops, the clutter cancellation ratio to CP is

201Og[Jy^-J-I dB

(2.8b)

where e is the average ellipticity weighted by the two-way antenna voltage characteristic. For example, for 25 dB clutter cancellation, 201og[(e2 + l)/(£ 2 — I)] = 25, s o e = 1.057.

2.7.14 Surface tolerance loss Reflector manufacturing tolerances, sag under the weight of the structure and wind loads which combine to distort the shape from true by 8 m rms, (root mean square; the square root of the sum of the squares of instantaneous values; standard deviation S) introduce a phase error: phase error =

rad

(2.9a)

consequent loss per plane, one-way = exp I

J numerical.

(2.9b)

\ XJ With imperfection in both planes the surface tolerance loss is squared: / 0.5

PpA < 10" 6 .

PD 0.5 is sometimes called 50 per cent blip/scan ratio, defined as the number of times an echo (blip) is detected divided by the number of sweeps within the packet.

False alarm probability of one in a million may sound very low, but it must be remembered that a noise paint can arise from any of the hundreds of thousands of detection cells on a half dozen sweeps per scan. Psychological or human factors (HF) such as fatigue, use of dim cursive displays, etc. can be partly allowed for in calculations by adjustment of necessary PD-

3.6.3 Digital conversion, detection cells So far, the radar signals and processes have been analog: 'Designating,1 pertaining to or operating with signals or information represented by a continuously variable quantity, such as spatial position, voltage, etc' Older radars were entirely analog, their detection strategy making use of the characteristics of long-persistence display tubes, described in Section 3.10. In the digital technology used in all modern radars, quantities take discrete values: 0, 1, 2, 3 , . . . , expressed as whole binary numbers 000, 001, 010, 0 1 1 , . . . , but nothing in between. Although analog circuits can perform arithmetical operations such as addition, subtraction and multiplication, it is far more convenient, quick, flexible, cheap, stable and accurate to use digital processing, adopting the technology of the computer industry. The first operation is to digitise the baseband data stream by an analog to digital converter; Figure 3.11. The analog voltage is repetitively sampled to give digital number 'snapshots' best representing the voltages at those instants. If the sampling or clock rate is less than the video bandwidth (undersampling), significant data is lost. If the clock frequency exceeds video bandwidth (oversampling), there is little loss but more and faster processing capacity is necessary. For pulselength say r = 0.1 |xs, video bandwidth ~0.5/r or 5 MHz so at least 5 x 106 samples/s are taken. Samples may have any amplitude from the noise background up to the echo of a large target. Together, finite clock frequency and digitising quantum or least significant bit (LSB) introduce a quantising loss. Apart from a little dead time before each sweep, every instant of the nominal 2.5 s scan time represents a slightly different basic element of surveillance area which may contain a target. In all there are some 107 area elements or detection cells, alternatively called range cells or bins, each identified by a unique address related to range and bearing and together forming a digital frame store. Economies may be made by reusing cells within areas containing insignificant content, but large memory is always needed. The integration process demands a set of detection cells for each beamwidth's worth of bearing, if the cell footprint is not to degrade that of the scanner beamwidth/pulselength. The azimuth might be divided into 512 bearing x 256 range cells = 1 3 1 000 cells, doubled for scan to scan correlation, but modern frame stores may contain over a million addresses. Only in the last years of the twentieth century did such large memory become economically viable. It is usual for cells to have equal angle resolution. Straddling loss occurs when small targets do not sit central to a cell, but sit astride a pair of cells to record unduly low strengths in each. 1

Shorter Oxford English Dictionary.

Analog to digital converter Zero range Range cells

Clock

Candidate A

Candidate B

Current scan Frame store Sweep 1

Sweep 2 Threshold voltage

Sweep 3

Sweep 4 Thresholding Sweep 5 Analog video from receiver

Sweep 6

Weak target?

Same target? Rejected after scan-scan correlation

Previous scan Frame store Sweep 1

Sweep 2

Sweep 3

Sweep 4

Sweep 5

Digitised return strength

Figure 3.11

3.6.4

Sweep 6

Signal processing. Digitised data is routed to detection cells within the frame store

Logical process of target detection

Figure 3.11 includes part of a simplified digital frame store, drawn as a matrix in range and bearing. For clarity a cut-down system is depicted. Thirty cells of range are shown, representing, say, from 10 to 14.5 km for pulselength 1 |xs. There are six sweeps in bearing, each sweep advancing by ^ scanner beamwidth, representing 0.65 km mean azimuth bracket at the range in question. Each cell contains thermal noise plus the echo and clutter content of about 150 m x HOm average sea area and the atmosphere above. For simplicity, cell capacity is shown as a mere 2 bits, content representing 0, 1, 2 or 3 analog baseband voltage units. The figure assumes modest noise or clutter, so most of the cells have count zero; a few have strengths of 1-3. Do cells having strength 1-3 represent targets? First, we examine the sweeps of the current scan by eye, for the human mind is good at pattern recognition. Looking at any single sweep in isolation, we may feel little confidence in drawing the line above

which we accept a return as valid, or put formally, set the threshold for detection declaration. Figure 3.10(d) shows such a threshold applied to the video signal. Examining the six sweeps as a set, pulse to pulse integration, gives a clearer picture. Returns of strength 1 seem so far below the strongest returns that we feel sure they must represent noise or clutter and are too feeble to have significant probability of being targets. We discard entirely all cells whose signal strength lies below threshold. Bearing in mind the steepness of the skirts of Gaussian distribution (Figure 3.5), it seems much more profitable to concentrate on the stronger returns, which are statistically much less likely to represent clutter spikes. Cells labelled 1, 5, 6, 17, 25 and perhaps 30 seem to form a significant cluster (candidate A). Another cluster, candidate B, contains cells 2, 7, 8, 11-14, 19-22, and perhaps 26 and 27. Cells 3, 4, 9, 10, 15, 16, 23, 24, 28, 29 and 31 seem random but might possibly represent small targets. In other words, choice of a low threshold risks numerous false alarms, but a high threshold risks rejection of genuine targets. Comparison with the previous scan's frame store appears to rule out candidate A because there seems no previous concentration of returns at or near the range and bearing in question - scan to scan correlation is poor. If A is a target, it must be subject to severe fading. Has a weak target at cell 4 been discarded? The claims of candidate B are reinforced: the previous scan contained a cluster at about the same bearing and range. Unless A is a very fast approaching target, only B is probably a valid target and we might well declare it, meanwhile watching future scans for confirmation. All that can be concluded from the evidence is: • • • •

there is high probability of a target at B; there is moderate probability of a fading target at A; several other weak targets possibly exist; increased SNR would reduce the uncertainties.

3.6.5 Machine detection The data processing system more or less replicates the mental processes outlined above in a formalised manner. To replace the mind's more subjective assessments, processing uses algorithms, defined and objective mathematical procedures, to squeeze the most information from the evidence quickly, tirelessly and rationally. We have seen that in isolation it is not possible to state with confidence whether a particular cell content represents signal or a noise/clutter spike. Optimum threshold level is usually computed to be several times average cell occupancy, which on the premise that most cells are devoid of targets, is a measure of the prevailing noise and clutter. The first step is to reject as clutter or noise all cells whose counts lie below threshold, called thresholding. The threshold stage can be analog, thus reducing the load placed on the digital convertor and signal processor. The threshold voltage is set in part by the processor, by reference to the clutter environment (generally assessed by the average cell contents) and partly by the operator's use of the gain control. In the example, the average signal, noise and clutter count is 53 in 180 cells, average 0.29. As the least significant bit in our simplified model is 1, the threshold might

be set at 1 (IV :0.29 V represents 10.75 dB, a reasonably typical value). Using 0 would let through all the noise and 2 would probably exclude too many genuine echoes. Signals or hits exceeding threshold form first-stage single-pulse target candidates. Clearly, detection is optimised by setting the threshold as low as possible consistent with accepting as high a false alarm rate (FAR) as the operator or system can abide. The noise/clutter density varies with range and other circumstances - Figure 2.6 shows how a squall may occupy only part of the playing area. It is therefore beneficial to juggle the threshold (or receiver gain, which amounts to almost the same thing) to give constant false alarm rate (CFAR). This is accomplished by a combination of methods: • • • •

•

swept gain, reducing gain at short range in a partially predetermined and partially adaptive manner; automatic gain control, averaging relative gain over the whole surveillance area; manual gain control, the operator setting IF gain (or threshold/logarithmic clipping levels) to give optimum display of a particular target; dedicated CFAR algorithms, which measure the average noise/clutter occupancy of cells near the candidate target, setting local FAR to maximum permissible by swept gain (or swept clipping level with logarithmic amplifiers); clutter mapping, where local clutter over each part of the playing area is regularly assessed, threshold being adaptively set for optimum FAR at each part.

3.6.6 Clutter map Particularly with VTS groundfast radar, it is feasible to memorise or map the locations of heavy clutter and adapt detection thresholds to match that locally prevailing, editing out stationary clutter from ground features, and much weather clutter. Much of the benefit of differentiation is obtained without loss of display quality. Clutter mapping is less effective when the radar platform moves rapidly through varying clutter density and is not yet common on marine radars. Even in the most crowded harbour, most cells contain only noise and clutter and are devoid of targets. The clutter map is constructed from the average count (discarding high values which are probably targets) of blocks of cells much bigger than a ship dimensions, taken over a succession of scans. The map is stored digitally and steadily updated at a rate sufficient to track clutter movement, e.g. of a rainstorm driven by the wind. The detection threshold at any part of the surveillance area is automatically adapted to suit the average local clutter by reference to the map. The map has to be very detailed to store coastal features and the strong clutter from breaking waves on the shoreline. One stratagem confines the playing area within the low-tide line, dumping echoes from elsewhere. This needs to be done with discretion; a VTS once puzzled why its radar had lost a ship, known to be within the harbour. The ship turned out to have drifted into the intertidal zone before grounding at high water in fog. Embarrassingly, as the playing area had been defined by the low-water line, the ship could not be displayed.

3.6.7 Detection decision process The detection threshold is set automatically to suit the prevailing clutter, but always with possibility of operator intervention. But it must be stressed that even the most advanced processing can never give certainty from corrupted and incomplete data having low SNR, as shown by Section 3.6.5. Figure 3.12(a) reproduces the cell matrix of Figure 3.11 more compactly. Figure 3.12(b) is after thresholding at 1 voltage unit. Cells having value 0 or 1 are dropped, all others being accepted as hits. Actual strengths are not stored, so the processor is compact, at cost of discarding some data. The detection criterion is some minimum number of hits per scan, sometimes called the m out of n criterion, here three hits out of six sweeps per scan. Candidates A and B each score three hits so would be declared as targets. The next increase of complexity is scan correlation, storing the previous scan's results, only declaring a target when both register some lower number of hits per scan, say 2. Targets with poor blip/scan ratio are likely to be rejected by scan to scan correlation. By adding further memory, the strength information can be stored, enabling the strength of each hit to be accounted for as shown in Figure 3.12(c). Again candidate B is declared, but with somewhat higher PQ. The full potential of correlation is not always realised, the designer sometimes being content to suppress interference from other radars using a combination of pulse-pulse timing jitter and a 2 pulse correlator (n = 2). Coherent systems also store phase data. Echo phasing jitters, particularly when SNR is low. Comparison of amplitudes during a scan with constancy of phasing sweep to sweep raises Pp. Scan to scan correlation can be used as before. In general we see that, for a given PFA> ^D *S raised if the following occur. • • •

• •

Many digitising bits are used. There is less quantising loss. The penalty is additional and faster memory capacity. SNR is raised. Cell size is reduced, needing bigger scanner aperture and short pulses, high bandwidth with the attendant additional noise, as well as additional processing power. Scan to scan correlation is used, again needing more processing power. The system is coherent, requiring a more complex transceiver.

Physically big targets sprawl over several adjacent detection cells. Particularly with short pulselength, even small targets may straddle a pair of cells. Probability of the candidate being valid increases when its immediate neighbours exceed average clutter and when the previous scan contained a cluster at or near the same position. Neither own ship or a target moves significantly during the 10 ms or so of the packet of sweeps within a scan, although their intensities may fluctuate. Receiver noise spikes meanwhile occur at random position. The processor has however to allow for fast targets traversing a couple of cells in the inter-scan period. Modern radars display targets with remarkably little clutter on the screen, even in adverse conditions. But it is important to realise that because the signal processor has

Candidate A

Candidate B

Current scan

Previous scan Digitised return strength

(a) Figure 3.11 redrawn Candidate A

Candidate B

Current scan

Hit if > 1 Hits per scan Previous scan

Hits per scan 2

2

2 or more hits each scan. (b) Scan to scan correlation, hit amplitude discarded Candidate A

Candidate B

Current scan

Counts with threshold Previous scan

Counts exceeding 6 each scan (c) Scan to scan correlation, hit amplitude retained

Figure 3.12

Digital detection. Adding sophistication improves probability of detecting valid targets while discarding false alarms

kept clutter off the screen does not mean that clutter ceases to degrade performance. Severe clutter necessitates raising the threshold to restore FAR to an acceptable level, so weak targets cease to be detected. Presence of noise or strong clutter always degrades performance. Declared targets are fed to a target register which memorises target locations and supplies a bright-up pulse to the display at the appropriate range and bearing. Radar data may be exported to other on-board instruments. For example, wave height is of particular interest to high speed craft which are not licensed to operate in extreme conditions. The Wavex [1] directional wave monitoring system calculates significant wave height from sea clutter signals extracted from the craft's standard navigational radar.

3,7 Additional features 3.7.1 Within single radar Relatively large ships viewed at short range may give paints approximating the target waterline plan, yielding valuable aspect data. The paints tend to be too small for easy viewing so some radars include a target expansion facility to double the apparent target size. The navigator needs to see at a glance the approximate course and speed of all targets. The target registers for the previous few scans are applied to the display at successively reduced brilliance, leaving a trail similar to a wake to indicate approximate course and speed. Control of the trail time frame or persistence can be provided as an operator control. When own ship yaws or manoeuvres, or the operator changes range scale or offcentres the display, the target register redirects itself to the correct part of the screen without smearing, the display remaining legible. The target may manoeuvre also, making it futile to integrate over many scans. Manoeuvrability assumptions have to be built into the scan-scan integration algorithm. How many adjacent range cells may be integrated depends on an assumption of maximum speeds of own ship and the target. A 30 knot ship ought to accept a HSC at say 70 knot (the upper limit of IMO's HSC Code, although some military patrol boats are faster). Maximum closing speed is then 100 knot (~49m/s). A HSC radar ought to accept another HSC, maximum closing speed 140 knot (72m/s). It would be counter-productive to accommodate aircraft at 200 knot. Setting the algorithm for unnecessarily high speeds lets in more noise cells and increases probability of false alarm.

3.7.2 Multiple sensors, track combiners The diversity principle seeks to improve detectability by observing the target in two or more decorrelated ways, where their clutter returns on any given sweep usually differ. Twin identical radars can have their scanners mounted at different heights or positions, or a single scanner can alternately use differing polarisations or transmitter frequencies.

Track combination is not current practice on shipborne dual radar installations, perhaps because the additional complexity outweighs the benefits. However, combination of tracks from two radar heads to form and display a single track from the composite data is standard practice on the larger VTS installations, enabling a target to be tracked seamlessly as it traverses the whole surveillance area. Considerable care has to be taken with accuracy of the basic radars, to ensure that a single target is not regarded as two, or two targets are not incorrectly merged or 'associated' as one. The first step is plot association, that is, make the decision whether a pair of plots on the two radars are from a single target or from a pair of close-spaced targets. This is not as easy as it sounds, particularly when SNRs are low, just when track combination would be most beneficial. Track combination is performed on digitised data within a dedicated computer. Cost-benefit analysis informs the choice from amongst the following alternative arrangements. 1. Each radar transmits a digitised but otherwise unprocessed data stream to the VTS, where tracks are formed in a central computer. Quasi-raw (relatively unprocessed) data can be displayed if required, and is preferred by some operators in certain clutter conditions, although it is nowadays hard to justify the assertion that an operator, however skilful, can improve on the performance of a well-designed trackformer. A disadvantage is volume of data, necessitating wide link bandwidth. On the other hand, the central computer can be duplicated for reliability at moderate cost and it is easy to adjust the tracking and combining algorithms to suit prevailing circumstances. Much grief can be (and has been) caused if data is discarded prematurely, e.g. if the link restricts echo dynamic range or overloads when clutter is severe. 2. Targets can be detected locally with detection thresholds set for fairly high PFAThis moderates the quantity of reported false alarms. Plots are reported scan by scan to the centre at moderate bandwidth, for subsequent further processing and track-forming. Weak targets may fail to be reported and be lost. 3. Tracks can be formed locally, only track combination from each outstation being central. Little transmission bandwidth is required to report formed tracks, but the operator is denied knowledge of local clutter conditions and cannot search for plots on which tracks have not been formed, such as new entrants to the area. Failure of a trackformer disables its outstation.

3.8

Display principles

The whole purpose of the radar is to communicate information to an operator by means of the display. The display, screen, or scope is the human-machine interface and is arranged to suit the operator - it must be user friendly. It should display as much as possible of what the operator needs - targets and associated alpha-numeric data - with as little extraneous clutter and noise as possible. Echoes displayed on the screen are often called paints or blips.

3.8.1 Display format On ships, IMO demands relatively large screens, 250 mm, to 340 mm active diameter on the bigger tonnages, to reduce eyestrain when alternately looking out of the window, viewing other bridge instruments and refocussing on the screen at moderate viewing distance, and to facilitate two persons viewing together, for example, the master and OOW when evaluating a manoeuvre. The very large 'conference displays' of some military systems are not used-perhaps merchant ships cannot muster enough deck officers! Screen area must have some influence on mental perception of echoes, but data is lacking. Current echoes or declared target plots are displayed as spots of light at scale range and bearing from the scanner position. This map-like form of display is called a plan position indicator (PPI); Figure 3.13. Targets are shown in polar or R9 0 (range, bearing) coordinates. The simplest PPI presentation keeps own ship or station at the centre of the display while all target paints, including coastlines, move past in relative motion. Ships' displays may be aligned to suit the traffic situation: North-Up, Ship's Head Up or Course Up (differing from head up if the ship makes leeway). Own ship may be offset from the centre to extend the view ahead. In the important True Motion mode, the display is ground stabilised and all targets and own ship move as across a map, resetting when approaching the display rim. VTS displays are of course always referenced to a fixed datum. They are sometimes aligned to the view from the station window - for example, the West Coast port of Vancouver, whose station lies to the North of the harbour, has found South-Up displays convenient. The operator measures target position relative to the scanner by intersecting a variable range marker (VRM) and electronic bearing line (EBL) over the plot of interest, digital readouts giving range and bearing relative to own scanner. Alternatively approximate position can be judged from a set of electronically generated range rings at say 1 nmi intervals and a bearing scale or pelorus (compass rose, nowadays

Figure 3.13

Display including radar data only: coastlines, targets (some with trails), offset with range rings, heading marker and copious alphanumeric information. Original infull colour. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK

Figure 3.14

Display with chart data superimposed. Original in full colour. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK

electronic rather than engraved, avoiding parallax) around the circumference. It is usually possible to lay a line between a pair of targets of interest and read off their relative range and bearing. A cursor can also be placed over any feature of interest, its coordinates being displayed alpha-numerically. Choice of presentation, although very important to the operator, rarely affects the detectability problem and we shall not consider it further. Displays of relatively unprocessed radar broadband video signals are called raw radar, but it is now usual to show processed or 'synthetic' information on the screen. Formerly, each radar had its own stand-alone display, the only non-radar data being a few short alpha-numeric statements of course, speed etc. Nowadays, partly because the display occupies prime real estate on the bridge, selected parts of the system electronic navigation chart (SENC) are routinely added to radar displays, Figure 3.14, and plots are exported as a radar layer within the ship's electronic chart and display system (ECDIS). There is scope for addition of AIS data and plots transmitted by VTS stations, although care must be taken not to present the operator with an inassimilable mass of material - information overload is dangerous, the mind tending to dump data in a rather arbitrary manner. The trend is for black box radars to export plots and tracks to multifunctional displays at operator workstations forming part of an integrated bridge system (IBS). Data fusion has been discussed by Lee [2] and the same fusion and association problems arise as when radar tracks are combined, Section 3.7.2. The radar market is much too small to support development and manufacture of special screens, so high quality computer and air traffic control devices are used, available in a restricted size range up to about 580 mm diagonal.

3.8.2 Cathode ray tube Many displays still use cathode ray tubes (CRT), a specialised triode valve or electron tube. Within the rear neck of an evacuated glass/metal conical envelope are three electron guns for the three primary colours, a single gun sufficing for the older

monochrome displays. Each gun has a red-hot metal cathode operated at a high negative voltage of about — 1OkV. Cathodes are coated with a mixture of oxides facilitating electron emission, under control of nearby 'grid' electrodes. Positivegoing grid bright-up voltage signals permit cathode rays of high-velocity electrons, ~ 100 |xA, to fly to the glass screen at the front of the tube, drawn by an earthed metal cylindrical anode (plate) within the neck. The rays are electrostatically focussed to sharp dots and can be steered by the time base system to any part of the screen by application of voltage to pairs of deflector plates (or by current to pairs of coils) surrounding the neck. The screen is made as flat as possible consistent with forming part of a pressure vessel and carries sets of electro-luminescent phosphor coating picture elements or pixels on its inner face which fluoresce in primary colours or the predetermined monochrome hue when struck by the beam, the display being intensity modulated by the grid signal. Colours, if used, are standardised by IMO (for navigational data) and IHO (International Hydrographic Organisation for charting features), differing for day and night illumination. Modern screens have very short afterglow and are scanned raster-fashion like TV screens, the bright-up signals coming from the frame stores, which here perform an R, 0 to Cartesian coordinate conversion, giving a flicker-free display, Section 3.9. Older CRTs laid down raw radar R, 0 video pulses sweep to sweep and scan to scan. Long-afterglow phosphors integrated the real time scan to scan to give a reasonably steady image, Section 3.10.

3.8.3 Other display devices CRTs are bulky and are rapidly being replaced in television and PC monitors by various kinds of flat screen low voltage semiconductor arrays, including liquid crystal displays (LCD), which are produced by the million. Application of a low voltage switches certain organic molecules between transparent and opaque states. In LCDs, a very thin film of the active liquid is sandwiched between glass sheets bearing a near-transparent pattern of conductors to form pixels, controlled by transparent thin film transistor (TFT) arrays. Backlit and colour variants are available. LCDs consume very little power. Long widespread in laptop computers, they were first taken up by the radar industry in small craft radars. Problems of available brilliance range, adequate area and wide angle of view are being overcome and price is falling. As a result, high resolution LCDs are replacing CRTs in new big-ship marine radars. Figure 3.15 shows part of a modern screen and shows the high resolution available. Advantages include low bulk, screen flatness, low power consumption and avoidance of high voltage. Sufficiently large screens or screen arrays for VTS stations are now becoming feasible, at a price. TFT screens drive each pixel continuously, not once per screen scan, improving brilliance and eliminating flicker.

3.9

Raster scan display

The modern flicker-free television-type raster scan display, Figure 3.16, has the phosphor applied as a fine pattern of (usually) coloured short persistence triplets

Figure 3.15

Portion of display. Target trails shown as varying tones in background. Original in full colour. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK Path of cathode ray 70 full-screen rasters/second Screen with pixel array of tricolour short persistence phosphors Target plot Brief pixel bright-up each raster Fed from frame store, refreshed each scan Electronic range and bearing markers for target position measurement Target trails from previous frame stores Presence and length controllable Own radar May be offset from screen centre to give longer view ahead Supports fast graphics and text in distinctive colours

Figure 3.16

Raster display. Shown on 12nmi range scale with lOOOpps. Target position is found by intersecting the variable range marker and electronic bearing line on its paint

of phosphor pixels in primary colours. Raster is Latin for rake. Operation is digital in character. The beam is steered in a quick zigzag path, raking the screen with about 70 complete rasters per second, like TV or PC displays, giving sufficient brilliance for viewing in full daylight. Use of a raster coarsens the basic R, 0 footprint at close range. Kelvin Hughes have experimented with spiral scans to maintain footprint so

detection cell area is proportional to range, but this has not so far fully caught on, perhaps because television display technology is unsuitable. Monochrome displays are sometimes used, see Chapter 2, Section 2.1.6, Figure 2.6. Oftener, full colour is used. The palette may be selected to suit daylight or night viewing conditions. The electron beams take up one of usually 16 or 32 digitally determined intensities, giving the pixel 16 or 32 grey scale (brilliance) values. The digital frame store data is converted from R9 0 to Cartesian format by a digital scan converter. The scaling and raster pitch are sufficiently fine for the eye to perceive the display as a flicker-free continuous range of tones and hues. Monochrome displays usually use a green phosphor, least tiring to the eye. The phosphors fluoresce during the electron pulse, but do not phosphoresce afterwards - they have short persistence, to cope with dynamic navigational situations and evolving alpha-numeric messages. To support text and chart data, and to avoid degradation of the echoes, radar displays need higher resolution than TV. The PPI itself occupies a circle or square field, up to 340 mm diameter, the whole field being 380 mm square as minimum on the bigger ships. The remaining space of the rectangular tube forms a convenient area for display of secondary alpha-numerics such as course and speed, control menus, etc. The pelorus is generated electronically on the display face, avoiding parallax when reading target bearings. Trackforming (generation of vectors) is performed electronically before paints are laid down, so any nonlinearities of scale caused by changes of deflection sensitivity near the rim of the tube do not affect calculations of CPA etc. The tube grids permit beam current to flow and a bright-up of appropriate colour to be generated only when the raster is at an address whose target register cell contains a target, or where secondary information is to be displayed. Each frame store cell is addressed each raster, although of course its input is updated only once per scan in an R, 0 manner. Scrutiny of a moving echo shows it to advance one step per scan. Target trails (see Section 3.10.1) are generated from the frame stores and are under the operator's control. Trails are shown in Figure 3.15. Necessary resolution is around a couple of million pixels. For example on the 12 nmi (22 200 m radius) scale, pulselength may be 0.1 |xs, equivalent to 15 m range cell. The diameter therefore contains 22 200 x ~ = 2960 cells and ideally the tube would have this number of lines with the same number of pixels per line, pixel size being 0.13 mm x 0.13 mm for 400 mm (16 inch) tube width. In practice, the eye cannot resolve such small pixels at normal viewing distance and pixels are made about 0.2 mm x 0.2 mm. About 1000 lines x 1500 pixels per line are used for ships' radar. Some large VTS displays have higher resolution, partly to support many small alpha-numeric target legends or 'tags'. Being reconstituted from stored and manipulated data, the display is synthetic, although there is a confusing tendency to reserve this term for tracks, terming plots as 'raw', even when they are the output of a processor. The screen is scanned frequently, giving enough brilliance for daylight viewing. The digital format of the input facilitates hooking-in secondary displays using local area network (LAN) techniques. At one time differing colours were used to indicate echo strengths. This practice has been discontinued, since strength is not navigationally significant. The phosphor persistence is too short for smearing when own ship manoeuvres or the range scale is changed.

Beside brightness, important features of raster scans include their ability to display in different colours, and quickly to amend: • • • •

the radar picture (plots and tracks); text, enabling targets to be tagged with identification symbols (also operator's menus for controls); radar graphics such as predicted tracks (from ARPA, etc.), range and bearing markers for position measurement, target alpha-numeric identification tags; non-radar graphics such as charts (from ECDIS, etc.).

By lessening the operator's mental task, raster systems give much more consistent detection performance and free the operator for the tasks that no machine can replicate - intelligent decision-making.

3.10

Cursive display

3.10.1 Raw radar Before digital computer technology evolved, echo plots were perforce displayed raw on a long-persistence monochrome CRT in PPI format, Figures 3.17 and 3.18. The display is polar, showing the received echoes in real time as the scanner turns, the beam (or 'strobe') being deflected by a motor-driven rotating coil or a fixed orthogonal pair of electromagnets, the latter facilitating off-centring of own ship's position. Long-persistence phosphors are available in few colours; many displays Time, jus, on 12nmi range scale Path of cathode rays. Sweeps synchronised with transmitter and scanner, ~ 2000 lines in ~2 s Three consecutive sweeps shown Trace flies out from origin at 12.35 us/nmi, with fast flyback Target plot Overlapping paints from sweeps in beamwidth merge Paint persists for several seconds Phosphor persistence leaves target trails, not controllable Uniform monochrome longpersistence phosphor coating Only supports slow graphics Beam sweeps synchronously with Tx pulse at t = 0, 1000, 2000,... JJS Own radar May be offset

Figure 3.17

Generation of cursive display. Suited to older radars without digital signal processors

use green or orange. The phosphor fluoresces momentarily when struck by the beam, after which it continues to phosphoresce with an afterglow for several seconds, not necessarily in the same colour. Cascade screens combine long- and short-persistence phosphor layers with sealed-in optical colour filters. In these older radars, each time the transmitter fires, the beam sweeps radially outward from own radar's position near the centre at a rate scaled to suit the transmission in a spoke-like or polar cursive manner, returns painting at scale range. Operation is wholly analog. There is no scan conversion and the screen is uniformly coated and not divided into discrete pixels. The sweeps rotate synchronously with the scanner, so the surveillance area is covered by a couple of thousand sweeps once per scan. The pelorus is engraved on a collar surrounding the display and is subject to parallax error, especially near maximum range, where curvature of the tube face is the greatest. Trackforming is generally performed manually using a reflection plotter, and any non-linearities of display scaling affect the trigonometry used in the calculation of CPA, etc. The trace on later sets is made less dim on short-range scales by addition of a store from which the trace is repeatedly painted. The small (~7 dB) brightness range of long persistence phosphors is augmented by a soft limiter in the video amplifier to better indicate relative signal strength, helping show targets in precipitation clutter and noise. Positive-going analog video bright-up pulses are applied direct to the CRT grid. Each pulse makes the phosphor at the scale location of the scatterer glow dimly, fading away after 20 s or so. If the bright-up is a clutter or noise spike, it is unlikely that the same point will be further brightened on succeeding sweeps or scans. But if the scatterer is a target, the same or an adj acent phosphor point is likely to be brightened on these sweeps or scans. The more hits, the brighter the phosphorescence; the phosphor integrates the returns sweep to sweep and scan to scan. Noise and clutter are not integrated and appear as dim speckles. The eye's excellent pattern recognition skill

Figure 3.18

Cursive display. Brightness variation as strobe sweeps display can be mesmeric. Decca 9GHz radar, 1.5 mile range scale, Inverness. Original monochrome orange. Author, 1983

then readily sorts echoes from noise, unless severe. Brightness is a measure of echo strength, within the limits set by the dynamic range of the phosphor, augmented by previous soft limiting applied to the video. Thus, the tube cut-off grid voltage performs the threshold function and the phosphor integration characteristic provides pulse to pulse and scan to scan integration. The phosphor persistence maintains the display between scans and automatically provides afterglow trails of target track history, whether this information is wanted or not. Spot brilliance to some degree indicates echo strength. Minimum spot size is ~0.5 mm, which may slightly degrade the display resolution when short pulses are used with a big scanner on a long-range scale. Radar sensitivity is optimised by biassing the grid just to extinguish the beam in absence of signal, adjusting the receiver gain to give faint background noise speckling, following the principle of setting false alarm rate to the maximum tolerable by the decision processor, here the operator's brain. The operator's mental pattern recognition capability is then used to sort the frequent noise or clutter spikes from faint but more persistent echoes. Long-persistence cursive displays well suited the earlier radars before modern computer technology was developed.

3.10.2 Cursive display problems The scan causes a rotating strobe of background brilliance variation, all too soporific when no targets seem in sight. Moving targets automatically leave trails of diminishing brilliance, useful unless they mask other targets, but of course not under the control of the operator. The display smears badly when own ship yaws or manoeuvres, unless set to North-up presentation, and also takes half a minute or so to clear after change of range scale or off-centring. Display of tracks is rather unsatisfactory because minor scan to scan track variations due to noise cause smearing. A phosphor point is illuminated once only per scan, yielding insufficient brilliance for daylight viewing, necessitating either blackout curtains or a viewing hood which precludes two or more persons viewing together and disaccommodates the eye. Attempts at more brilliance lead to an objectionably bright 'initial flash'. Radars of the cursive era take feeds from the ship's log and compass, but otherwise tend to stand in proud isolation from other bridge equipment. Indeed, the earliest bulky equipments like the BTH RMS-I came in their own special cabin, the operator telephoning voice-told plots to the bridge in the tradition of the crow's nest lookout. Later, a junior officer acted as radar observer at the back of the wheelhouse. The dim display and its daylight screening preclude one-man bridge operation. Tracks are drawn by hand on an anti-parallax reflection plotter over the screen. The plotter is a semi-silvered transparent screen of opposite curvature to the tube face. Labour-intensive and permitting only a few targets to be followed, at least this chore focusses the operator's attention on nearby shipping movements. Display of alphanumeric data is difficult. One manufacturer (AEI) went so far as to provide a separate 400 mm short-persistence green alpha-numeric display, superimposed visually on an equally large orange long persistence radar tube, the pair being combined by a half-silvered mirror, hardly a compact arrangement. It was soon withdrawn.

Continued observation of a cursive system in strong clutter demands close concentration and is tiring. The eye takes time to accommodate to the dim display. Gain and brilliance controls must be kept in careful adjustment for good results. It is all too easy to take the lazy option - operate at high brilliance, low gain, fine for strong echoes, eliminating noise and clutter - unfortunately setting the grid bias threshold so high that small targets are eliminated as well.

3.10.3 Detection performance Under ideal conditions, raw radar detection performance is little inferior to that of modern equipment and the same detectability calculations can be employed, with an operator correction to account for: (a) inappropriate control settings and (b) nonperception of targets displayed, perhaps weakly, on the screen. These human factors are difficult to quantify. They may be allowed for by assuming that the probability of detection threshold is high, or by addition of an operator loss term, L op , in the radar range equation. The following has been adapted from a suggestion of Skolnik [3] but, as with all psychological effects, precision is impossible:

L0P-IOIo8(^dB.

(3.5)

For example, if desired probability of detection is 0.9 or 0.5, L o p ~ 2.0 or 4.5 dB, respectively.

3.11

Plots on the screen

Figure 3.19 depicts the main classes of target discussed in later chapters and encountered by marine and VTS radars, with an indication of the appearance of their plots. A short-sighted person using a searchlight on a clear dark night sees these targets in much better detail than can radar, which displays only those scatterers which reflect significant energy towards the scanner. No radar has remotely as good bearing discrimination as the eye and only frequency diversity is in any way analogous to colour vision. Small scanners, which cannot resolve to better than about 4°, display small targets as radial arcs several degrees wide, T on the figure. The best VTS scanners have about 0.4° resolution and reproduce small targets as crisp points. However, unlike the eye, radar does accurately measure range. Most radars have similar range discrimination, between about 15 and 150 m according to pulselength. Poor angular resolution and detection cell size of marine radar, together with uncertainty as to which parts of the target are currently reflecting, usually preclude reliable indication of target aspect, the direction of vessel centreline, which tide streams, etc., may force off the radar track or course made good. This is unfortunate, for the Collision Regulations are written round aspect, conventionally determined by viewing side and masthead lights. Some VTS systems do have sufficient resolution to display aspect at short range, useful when the operator wishes to see a ship come off its berth, for example.

Ship beam-on Extended targets Rolls in radar plane Rollg Coastline Inland mountain

Ship bow.on n Q r m a l tQ

^

lmQ

Surf or ice

Displayed echoes are shown in heavy line Electronic measurement aids Range Ring or Variable range marker (VRM) Pelorus scale. 000° = North or Ship's Head Electronic bearing line (EBL) VRM and EBL are placed on target T to measure its range and bearing Point targets Unaided small craft or buoy Viewed by small scanner Viewed by large scanner Viewed by long pulse

Range

Paint trace may not represent target shape Active targets Target location Racon code N Sidelobe responses (possible with any target) RTE Ramark SART code 12 dots Heading marker

Feeder ringing Precipitation clutter

Figure 3.19

3.12

Thermal noise

Sea clutter Running rabbits Clutter, noise and interference

Own radar May be offset from centre Measures bearing from scanner angle and range from echo delay Detection cell (not displayed)

Radar display content, showing the different classes of target plot, clutter and noise. Detectability calculations differ for the passive and active targets shown. The heading marker shows the fore-and-aft line, not the course made good

Radars for special purposes

3.12.1 High speed craft Fast ships find encounters with other vessels develop so rapidly - at several km/minute - that bearing precision is secondary to the need for low display information time lag or latency. HSC (high speed craft) radars are obliged to comply with specification IEC 60945-2. They use near-standard 3 or 9 GHz marine radars with lightweight scanners rotated fast - IMO minimum 40 rpm - so targets are updated as often as possible. Aperture is 2.7-3.6m (9-12 ft) at 3GHz or 1.2-1.8m (4-6 ft) at 9 GHz; elevation beamwidths are 20°-25° and gains are around 25-28 dB on each band. The relatively low mounting height helps reduce sea clutter, aiding the essential task of detecting small targets at moderate range quickly. The low mounting is detrimental to long horizon range, which to these manoeuvrable craft is of minor importance. The relatively small scanner apertures counter the high rotation rate; number of pulses per beamwidth remains fairly conventional and so does the

signal/(noise + clutter) ratio. The stringent requirement for range discrimination of 35 m laid down in the HSC Code necessitates short pulselength and many range cells.

3,12.2 Warships The main surveillance radars carried by warships are dedicated to military tasks and not ordinarily used for navigation. Navigation radar is also carried. Although particularly robustly constructed to withstand combat shock and having some special features, particularly in the display area, it is in essence a civil marine radar, with similar transmission characteristics. Not only is this format best for the job and familiar to civilian pilots who may be taken from time to time; but it gives an identical signature to a merchant ship, enabling the warship to mingle unobtrusively into the marine environment without breaking military-radar silence or disclosing its identity to hostile SIGINT (signals intelligence). Warships on exercises in the Mediterranean are understood to have moved about undetected by 'hostile' forces for several consecutive days. Surfaced submarines manoeuvring in port areas may deploy on the sail a small portable 9 GHz radar, again with a civil marine radar emission signature.

3.13

Calibration

Radar failure may be catastrophic but is more often gradual, as the magnetron wears out after ~5000 h life, as the mixer diodes become less efficient after constant bombardment from mismatch reflections, as internal circuits drift out of tune or other adjustment and if the feeder suffers damage allowing water to seep in. Loss of performance can be too slow to be noticed by the operator, or new operators joining ship may be unaware of the radar's true potential. Besides arranging for regular servicing by qualified technicians, operators should make routine performance checks, note results and compare with previous records. Wylie [4] strongly advocates maintenance of a formal radar log in which operating experience is recorded, devoting a whole chapter to the topic. Some simple checks should be made regularly. • • • •

Unless the sea is calm, some sea clutter should surround own ship when the radar is operated on full gain, long pulse, without differentiation. Any visible shipping or coastlines should be checked for echoes. If two radars are carried, loss of small close targets on one alone is a sure indicator of trouble. Built-in checking facilities should be used. These vary in complexity and the following summary is not exhaustive.

To confirm whether the transmitter is radiating full power and that receiver sensitivity is normal, a metallic chamber called an echo box was sometimes mounted near the scanner, usually just below. A colleague of the author attracted much ribald comment by trying copper float balls from water cisterns as echo boxes. Unfortunately, the equatorial joints proved poor conductors and loss was excessive. A small antenna such as a horn picked up a sample of radiated transmissions when the scanner

came through echo box bearing, placed in a blind arc or astern. A small motor-driven paddle often broke up any frequency-dependent resonances to make the feather length independent of exact magnetron frequency. The box formed a multimode resonant cavity of fairly high Q factor. The microwave pulse rattled round within it, reflecting back and forth as in a mismatched feeder. The horn radiated the 'echo' for several microseconds as the reflections decayed. Some was picked up by the scanner and displayed as a performance feather or plume on box bearing. Length was a kilometre or so and gave a measure of system overall performance, including scanner and feed. Nowadays the echo box is usually lightly coupled to the scanner feed and has preset electromechanical tuning to magnetron frequency. Its echo displays on all bearings as a sunburst around own ship; radius is a measure of the system excluding scanner and feed. For this, a small neon lamp is mounted on the static housing of the scanner drive. On each scan, near field spillover radiation should ionise the neon, causing a circuit to impress a plume at neon bearing, length indicating radiated power and acting as a transmitter monitor. The sunburst is referred to as a receiver monitor, although of course it also partially monitors the transmitter. Although these arrangements do not pretend to be precise, they have two great merits: they check the whole radar system including the scanner, and they are independent of the system. However, they cannot monitor the environment and loss of long-range performance due to adverse refraction, ducting or precipitation attenuation is not indicated. Receiver sensitivity can be precisely calibrated by introducing wideband noise of known amplitude, the power needed to double existing noise power equalling the system noise power. Although included in some VTS systems, marine radars do not normally include such complexity. VTS and coastal surveillance operators should identify a few weak static reference targets at moderate range and clear of blocks of clutter. Examples might include electricity pylons or lighthouses. Bearing, range and subjective echo strength should be noted as a routine. Range or bearing changes clearly indicate display error in the radar. Some strength variation inevitably occurs with weather conditions, tide height, etc., but persistently poor echoes may well indicate a radar malfunction. Buoys should not be used, particularly when subject to currents strong enough to set them over and change their RCS. Very distant targets are too much affected by atmospheric attenuation and refraction to make reliable calibration aids. It is harder for ships to make such checks, but liner trades might profitably make a point of listing a few calibration marks in each regular port of call.

3.14

References

1 MIROS, A. S.: 'Norway', reported in Speed at Sea, February 2002, p. 11 2 LEE, R. G.: 'Future bridge navigation', Seaways, The International Journal of the Nautical Institute, 2002, p. 9 3 SKOLNIK: 'Introduction to radar systems', Eq. (2.57) 4 WYLIE, F. J.: 'The use of radar at sea' (Hollis & Carter for the Royal Institute of Navigation, 5th edn.), chapter 13

Chapter 4

Echo strength in free space 'A little knowledge is a dangerous thing.' Alexander Pope, An Essay on Criticism

4.1

Introduction

This chapter considers transmission between radar and target in an unbounded vacuum. In this hypothetical free space, environmental effects are ignored; there is no atmosphere, weather, Earth surface or other tiresome practicality. We shall derive basic forms of equations, the radar range equations, describing the energy reaching the target on the transmit leg and echoing back to the radar on the receive leg of its journey, on which later chapters will build when examining practical conditions including the environment. Application of free space equations directly to the real world without allowance for environmental effects often leads to gross errors, especially when range is long so rays traverse a lot of atmosphere. Throughout this chapter we assume the target remains of constant electrical size and is physically small enough to behave like a geometrical point. In free space, energy radiated from a source such as a lamp or radar transmitter propagates in straight lines at the speed of light without loss; as explained in Chapter 2, Section 2.7. Doubling range, R, doubles the height and width of the beam and reduces the energy density to one quarter its original value, so energy density oc I/R2. This inverse square law, which applies to light and sound as well as radar waves, is the reason why distant targets are illuminated weakly. Echoes from ordinary passive objects again suffer the inverse square law, making echo power reaching the scanner follow an inverse fourth power law, echo oc \/R4. Doubling range, by an octave, reduces echo power to ^ (—12 dB) its former value. We now analyse transmission strengths more formally, at first ignoring radar losses and using numerical quantities, later changing to decibels.

4.2

Radiated power density

Chapter 2, Section 2.7.1, Eq. (2.6) showed that when a source radiates power P W isotropically at wavelength A, power density, d, measured at range R m is d = P /(AnR2) W/m2 of transverse cross section. If the isotropic radiator is replaced with a 'perfect' lossless directional antenna of beamwidths 0, 0, effective mouth or aperture area A m2 and gain G (as we shall only be considering conditions on beam axis, we write G for G max in this chapter), the energy is concentrated to produce a stronger power flux density over a smaller solid angle Q = Ocj) steradian. The basic antenna theory in Section 2.7.2 shows that on beam axis G = An A/A,2 (Eq. (2.7e)). Including a transmitter loss Lt, and substituting in Eq. (2.6), power density on the transmit leg falls with range according to the inverse square law:

4.3

Passive reflector; radar cross section, radar range equation

4.3.1 Radar cross section How well a passive object reflects energy back towards the radar depends on its size, shape, aspect angle to the illuminating radar and material (e.g. whether conductive metal or insulating plastic), as well as the radar wavelength and polarisation. A sphere has the unique property of looking the same from any aspect. Unlike almost all other shapes, its radar cross section (RCS), radar echoing area (REA) or [radar] cross-sectional area (CSA) is uniform, not fluctuating with the angle of aspect. Unusually, the proportion of incident energy reflected does not depend on wavelength, provided the sphere is in the 'optical region' where it is at least several wavelengths in circumference. These properties suit the sphere for use as a reference reflector and lead to the definition of RCS of an object: 'RCS is the proportion of incident energy reflected back in the direction of the source, relative to the proportion reflected by a replacement perfectly conducting sphere of cross-sectional area I m 2 ' . Spheres reflect isotropically (in all directions). RCS, cr, equals the cross-sectional (silhouette) area: a=nr2m2.

(4.2a)

From the mechanism causing a sphere to reflect, detailed in Chapter 7, RCS can also be defined as

o =

(power per unit solid angle scattered in a specified direction and polarisation) (power per unit area incident on the scatterer from the specified direction and polarisation)

. (4.2b)

RCS of practical targets often fluctuate, for example as they roll in sea waves. Fluctuation is considered in Chapter 12. Meanwhile, unless stated otherwise, we assume RCS and echo strength are the average values presented to the radar. More complicated shapes have RCS only very roughly similar to their silhouette. For example, RCS of a flat conductive plate falls rapidly when turned oblique to the radar. Much time and computing power is needed to calculate RCS of practical targets of even moderately complex shape. RCS of point targets is discussed in Chapter 7, with ships and other extended targets in Chapter 10.

4.3.2 Two-way free space radar range equation On the receive leg, total power reflected towards the source is

The power density, d\ reaching the scanner mouth is calculated by considering the target as a transmitter of power Prefl. Applying Eq. (4.1): ,_ ^ _ JaPGnAnR2Lt)] 2 " 4nR "" 4TTR2

_ PGa " (4jr)2R*Lt

2 (

'

j

We denote the echo power delivered to the receiver by the scanner as Se(FS 12) > subscript (FS) indicating free-space conditions and (12) that both transmit and receive legs are included. The signal fed to the receiver is aperture x density Se(FS12) = Ad'.

(4.5) r

Substituting in Eq. (2.7e) for A, in Eq. (4.4) for d and adding receiver losses L1

**»«> = ^ W ^ L ,

= PG^\AnT'R-\LtL^

W.

(4.6a)

This form of the radar range equation connects the radar parameters (such as transmitter power, scanner gain, received signal strength) with target and external factors (such as RCS and range). There are numerous variants. For example, the equation can be written to give R in terms of receiver bandwidth, noise figure, probability of detection, etc. To be exact, Eq. (4.6a) is one form of the two-way radar range equation for a passive target in free space. As expected from considerations of conservation of energy, it confirms Section 4.1 that echo power follows an inverse fourth power (R~4) law. Note that for a given signal strength Se(FSl2)> operation at longer range demands an increase of radar parameters P or G, or of target size a: • •

doubling P or a increases R by 21Z4 = 19 per cent doubling G (e.g. by doubling scanner area A, say by doubling aperture width) increases R by 2 1//2 = 41 per cent, because the benefits of high gain accrue on both transmit and receive legs. Eq. (4.6a) can be written in terms of aperture area, A, rather than gain: Se(FSi2) = o A2 P (47T)-1 X- 2 ^- 4 ILtL 1 ]" 1 .

(4.6b)

This highlights that for constant aperture, doubling wavelength k reduces R by 41 per cent for a given signal strength. In practice, a tends to fall at long wavelength and multipath further also affects performance. The range equation predicts that halving scanner gain, G, reduces echo strength to one quarter. However, low G means more solid angle is illuminated, in general raising azimuth beamwidth, giving more echoes per scan. Chapter 3, Section 3.6, indicated that this improves signal to clutter ratio, partly recouping the reduction in echo strength. We shall encounter several similar secondary effects through the book. The range equation merely indicates echo strength, not echo detectability - which also involves competition from noise and clutter - and is just the first step of the road leading to calculation of whether a given target will be seen by a particular radar under particular circumstances. In basic radar theory, detectability is ultimately dependent on the mean power transmitted, P m , independent of the form of modulation. The reasoning is as follows. We rewrite Eq. (4.6a) as

^ 4 = PG^X\Anr\ULA-\

( 46 c )

Se(FS12)

We replace Se(FSi2) by Si, the minimum single pulse which can be detected and put Si = nkTBs with the meanings of Chapter 3, Section 3.3.2, Eq. (3.2a);,? = minimum SNR for detection. If there are Af pulses in the packet and these are integrated within a coherent system, the minimum packet power which can be detected, SN , is inversely dependent on N:

Si SN =

^

nkTBs =

IT'

If pulselength = r and pulse repetition frequency = F , and assuming a matched filter so B = 1/r, P1n = P r F ,

so P =

^

.

Substituting in Eq. (4.6c) for maximum detectable range Rmax

The terms in bold type are independent of the form of modulation, and N oc F, so the B, F and N terms cancel and 4

*-

a

P m G 2 < rA 2 (47r)- 3 [L,L r ]- 1

^fS

'

(4 6d)

-

which is dependent on the mean power but does not contain terms in P , F , r or B which depend on the form of modulation. Whether P m (for marine radars

PM ~ 10 W) is radiated continuously as in a broadcast radio transmitter or is concentrated in short pulses as in marine radar is basically a matter of practical convenience. It is possible to make continuous-wave radars, primarily measuring radial velocity by Doppler frequency shift, rather than range by time delay as in marine radar. Range is then determined by the phase shift of a video-frequency amplitude or phase modulation superimposed on the transmission. Such radars are ill-suited to marine use and will not be discussed until Chapter 16. Nevertheless, it is well to be aware that the current marine/VTS radar format is neither essential nor some unique arrangement ordained by heaven. The format could be replaced should need be, for example, as pressure intensifies on the electromagnetic spectrum. Indeed, telecommunications users might like to consign pulse radars with their extreme EIRP (equivalent isotropic radiated power, Section 4.5.2) to a place far from heaven.

4.4

Active target

Active targets receive signals from the radar, process them and retransmit using some electronic device, Chapter 8. They have a receiving antenna, aperture Ax and gain Gx. Published parameters of active targets include their internal losses, so these do not feature separately in the range equation. Using similar arguments to those leading to Eq. (4.6b), the one-way radar range equation between a transmitter and receiver in free space is:

This equation follows the inverse square law. We can adapt it for the response leg, from the target of transmitter power Pu transmitting antenna gain G t and no losses. We include radar receiver loss, to give the signal strength at the radar receiver from the response transmission. It also follows the inverse square law:

4.5

Range equations in practical form

4.5.1 Extensions for practical environment The next chapters will examine environmental effects, showing the atmosphere introduces a loss, LA, dependent on range and that multipath interference modifies the free space signal by a multipath factor M in a range-dependent manner. These effects apply to each of the radar-to-target and return legs. In free space LA and M=I numerically (0 dB, no loss). It is convenient to introduce the terms here although we cannot yet evaluate them. We drop the free space (FS) subscript as the real environment is intended and convert to the decibel forms frequently used in later chapters.

4.5.2 Full radar range equation, dB When the terms are all expressed in dB or dBW, Eqs (4.6) and (4.7) become: Practical two-way. Echo received at radar from passive target: Se = Se(FS12) ~ 2LA + 2Af = P + IG + 201OgX - 30 log (An) + o - 40 log R - Lx - Lx - 2L A + 2M dBW.

(4.8)

EIRP, /3EiR, is the transmitter power needed to give the same flux density if the directional scanner were replaced by an isotropic radiator of unity (0 dB) gain and is a measure of the radar plus scanner's ability to direct power to the target. /^1R = p + G -Lx dBW.

(4.9)

Eq. (4.6a) becomes: Se = ÊiR + G + 20 log X - 30 log(4;r) + a - 40 log R - Lx - 2LA + 2M dBW. (4.10) Practical one-way. Interrogation received at an active target (Eq. (4.7a)) is % = %(FSi) - L A + M =/> + G - Lx + 201ogX - 201og(4;r) + Gx - 20log/? - L A + MdBW

(4.11a)

or % = /"Em + 20 log X - 20 log(4;r) + Gx - 20 log R - L A + M dBW. (4.11b) Practical one-way. Response received at radar from an active target (Eq. (4.7b)) is Sx = Sx(YSi)

-LA-T-M

= PX + G + 201ogX - 201og(4;r) -J-Gx- 20log R-Lx-Lp,

+ MdBW (4.11c)

or, where PtEiR is the target EIRP (PtEiR = Pt + Gt dBW): Sr = PtEiR -T-G-T- 201ogX - 201og(4;r) - 20logR - Lx - L A + MdBW. (4.1Id) 4.5.3

Reduced

equations

The radar terms shown bold in the above equations can be lumped together as a figure of merit, F. Denoting range in km units, Ry^n, to avoid inconveniently large numbers, Fi2 is the free-space echo at the radar from a target with unit RCS (a = 1 m 2 ) at 1 km

(^km = 1.0). Fi2 is a figure of merit for the radar over transmitting and receiving legs. The 120 term reflects use of km, 100(T4 :1 = -12OdB: F 12 = P + 2G + 20 log A. - 301og(47r) - 120 = P + 2G + 20 log A. - 153 -Lx-Lx

-Lx-Lx

dBW.

(4.12)

Using figure of merit, Eq. (4.10) becomes Se = F 12 + o - 401Og^k1n - 2L A + 2MdBW.

(4.13)

Similarly, for one-way transmission, we get a reference equation for the interrogation reaching the target, where Fi is a radar transmitter figure of merit. The —60 term reflects conversion to km. Stgt = F 1 + Gx - 201Og^k1n - 60 - L A + MdBW,

(4.14)

Fi = P + G + 201ogA - 201og(4;r) - 60 - Lx = P + G + 20 log A - 8 2 - L t dBW.

(4.15)

Where F 2 is the radar receiver figure of merit, the response at the radar is: Sx = F2 + Pt + Gx - 201Og^k1n - L A + MdBW.

(4.16)

F2 = G + 20 log A. - 201og(4jr) - 60 - Lx = G + 20 log A - 82 - Lx dBW. (4.17) The radar range equation includes the following values worth noting: 20 log X - - 2 0 'dB'(3 GHz band, X - 0.1 m), or 20 log X - - 3 0 'dB'(9 GHz band, X - 0.032 m) 101og(47r) ~ 11.0'dB'.

4.6

Calculations and graphs

The range equation is so important that it is worthwhile illustrating how it is used for calculation of echo strength and graphical depiction of variation of echo strength with range.

4.6.1 Fixed range example Suppose we wish to find the free-space echo from a navigation buoy of RCS 10 m2 at 10 km range received by a typical deep-sea ship's 9 GHz radar having: / = 9400 MHz

giving X = 3.19 cm, 25 kW transmitter pulse power, scanner gain 1260, total transmitter loss 4 dB, total receiver loss 5 dB. For comparison we set out a range budget, with linear and decibel alternatives, Table 4.1. Splitting the decibels into positive and negative columns helps avoid minus sign blunders, so easy with hand calculation. This method is well suited to initial 'order of magnitude' tests to check feasibility of a proposed system, or as a cross-check for gross errors within more detailed calculations - computers are very accurate but work on the garbage in, garbage out principle, never questioning inputting blunders. For this radar Fi2 = —85.9dBW. Multiplying and dividing numerical values, -Se(FSi2) = 2.572 x 10~12 W. Adding and subtracting decibel equivalents (expressed to nearest 0.1 dB), Se(FSi2) = —115.9 dBW, which converts by the methods of Chapter 2, Section 2.1.7 to 25.7 x 10~12W. The difference is a trivial rounding error of 0.1 percent. The calculated echo power of less than a hundred-thousandth of a microwatt would probably be detectable in free-space conditions, but environmental effects such as Earth curvature might prevent detection in practice.

4.6.2 Graphs Calculations as Table 4.1 for a spot range do not reveal the full story. It is worthwhile preparing a graph of signal strength versus range to indicate whether signal is changing rapidly and so might be unduly sensitive to parameter variations. The 'obvious' way to do this is as follows. 1. Draw linear range (abscissa, X-axis) and power (ordinate, F-axis) scales on a sheet of ordinary linear graph paper. 2. Calculate (as Table 4.1) echo strength at several spot ranges. 3. Plot the echoes as a series of points at the proper ranges and powers. 4. Insert the minimum detectable signal curve. 5. Draw a smooth curve through the points, freehand or by French curve. The result is Figure 4.1. The echo curve falls sharply at short range and less sharply as range increases. We know from Eq. (4.6a) that it has the form power oc R~4, but this is by no means obvious from viewing the graph. The echo power curve in itself is only part of the story, which is why a curve of the radar's minimum detectable signal (MDS), the minimum echo strength needed for detection, has been added. For simplicity, MDS is here assumed 0.5 x 10~12 W irrespective of range; in practice it would vary. At short range, the echo exceeds MDS and the target is detected. At long range, the echo falls below MDS and is undetectable. The intersect gives maximum free-space detectable range or first detection range, which can be scaled off the graph as 15.1 km. For most purposes this presentation is tiresome; unless the range bracket of interest is less than about 2:1 the curve clings close to the axes and is difficult to read. Changing to a linear decibel power scale - equivalent to logarithmically in watts -in

Table 4.1

Range budget by linear and decibel

methods

Free space Quantity

Numerical value

Dimensionless except as stated Equation Eq. (4.6a) P 25 000 W G2 1587 600 X2 Conversion 1/Lt 1/Lr Operation

0.00102m 2 (l/47r) 3 /10 1 2 1/2.51 1/3.16 Multiply

dB (pos)

dB (neg)

Eq. (4.8) 44dBW 62 dBi

Eq. (4.8)

Notes

12602 = 1587 600; 2x31 =62 (0.0319)2 = 0.00102 Negative dB as < 1

Add

-29.9 -153.0 -4.0 -5.0 Add

106

-191.9

AdddB (+ve) and dB (~ve) columns

-85.9

-85.9 dB = 2.5704 x 10" 9 There is a small rounding error

Risk of decimal point error when using numerical values

\t

F12

2.572 x 1(T 9

o I//? 4 (10km)

10 m 2 1/104

1OdBm2 -40 10

^r(FS12)

Multiply 2.572xlO" 1 2 W

-125.9

Add dB (+ve) and dB (-ve) columns

\ -115.9dBW = -120 + 4 . I d B W = 10" 1 2 x 2.570 = 2.57 x 10~ 1 2 W

Figure 4.2 opens things up a bit, but some disadvantages remain: • • • •

the curve is tedious to calculate and draw the law relating echo strength to R is not revealed the curve becomes very cramped at short range it is not easy to change a parameter, for instance target RCS or transmitter power.

Figure 4.3 overcomes the problems. As in Figure 4.2, power is scaled linearly in dBW. But range is now also to a logarithmic scale, so each cm now represents a certain range ratio. This linearises the echo strength line, which falls —40 dB (power ratio 1:10~4) when range is increased by a factor of 10, immediately revealing the R~4 law (S ex R~4) followed by the echo.

2. Plot calculated strengths at spot ranges

Echo, W

Power, WxIO" 12

3. Draw smooth curve through points

4. Add MDS threshold

5. Read off intercept with MDS

1. Draw scales

Figure 4.1

Range, km

Echo strength versus range, linear power and range scales. Echo strength has to be plotted from a series of values calculated at judicious ranges. Note how rapidly power falls at short range. Law is not obvious and short ranges are cramped. The maximum detectable range intersect at 15.1km is difficult to determine accurately

Echo, dBW

Scale

Echo, 1OdBm2 target

Range, km

Figure 4.2

Echo power in dBW, linear range scale. Less cramped than Figure 4.1, but still inconvenient. Draughting procedure similar to Figure 4.1.

decade

Echo, 3OdBm2 target (Light line) down

Octave Echo, 1OdBm2 target (Heavy line)

Power, dBW

Echo, 4 dB m2 target (Light line)

Slope -40 dB/decade = -12dB/octave Entry p< >int: RCS 0 dl I m2 at 1.0 km

Scale 2:1 range change Sketching steps

Centimetres

Figure 4.3

6

Range, km, log scale

Logarithmic range scale, otherwise as Figure 4.2. Simple to draw and instructive to use. Linearises echo/range law, revealing that echo is changing —40dB/decade and so following R~4 law. Easy to assess changes to parameters, for example changed RCS, light lines

The procedure is easy, accurate and quick, with only a single calculation. 6.

If log graph-paper is not at hand, it is easy enough to mark off plain paper with a range axis. If interested in ranges between 0.1 km and 100 km, which is three decades, with graph width 15 cm to give 5 cm/decade, mark 0.1 km at the start, 0.2km at 1.5cm (5log2 ~ 1.5), 0.5km at 3.5cm (5log5 ~ 3.5), 1.0km at 5 cm, and so on to 100 km at 15 cm as shown in italics.

As with Figure 4.2, mark the vertical axis as echo strength linearly in decibels to a convenient scale, say 1 cm per 10 dB between say —160 dBW at the foot of the page

and O dBW near the top. Few radars will detect signals weaker than —130 dBW, but it is convenient to take the graph down further to aid construction of the curve. Draw construction line AB in a corner at slope —40 dB/decade (R~4 law). Calculate Fi 2 per Eq. (4.12) or Table 4.1 with R = 1000m and or = OdBm 2 . This gives the reference echo from a 0 dB m2 (Im 2 ) target at 1 km. 9. Enter on graph (point C). 10. Enter point D, a dB above C (here 10 dB), to represent the echo at 1 km from the 1OdBm2 target. 11. Draw a straight line parallel to AB (a navigator's parallel rule is handy) through D, produced to the sheet borders. The curve, of the form y = JCZ, becomes linearised with slope z9 so log y = z log x. This is the echo from a 10 dB m2 target in free space. 7. 8.

The graph is no longer cramped. To examine the effect of changing a parameter, we merely slide the curve vertically up or down by the appropriate number of dB. For example, an echo of a ship of RCS 3OdBm2 (1000 m 2 ) lies a further 2OdB up and a dinghy of RCS 4 dB m2 (2.5 m 2 ) lies 6 dB down from our 10 dB m2 buoy (light lines). The intercepts with MDS indicate the ship has maximum free-space detectable range 47.5 km and the dinghy 10.6 km. It is equally easy to judge the effect on detection range of changing MDS, e.g. when using another pulselength/receiver bandwidth combination. One merely slides the MDS line up or down by the appropriate number of dB.

4.6.3 Computer spreadsheet and charting Using a personal computer (PC), life is easy. All we do is compile a simple spreadsheet with cells for each of the terms of whichever of Eqs (4.8)-(4.11) suits the system, using either numerical or dB forms. A column of a hundred or so ranges, incremented from the lowest to the highest of interest, is followed by a column containing the chosen equation. The PC can then automatically 'chart' the relationship. Most Windows computers have EXCEL spreadsheet facility, which permits computation of logarithms, allowing quick numerical/dB swapping. And the chart can scale itself logarithmically, so if we produce a Figure 4.1 lookalike which turns out to be cramped, a Figure 4.3 version can quickly be generated. To try the effect of changing a parameter, we merely enter the revised value in the appropriate cell. The signal strength graphs in this book were generated in this way. The IEE website (www.iee.org) includes comprehensive spreadsheets which include environmental effects. Chapter 14 gives full details. It is all too easy to enter an incorrect value in one of the many cells necessary to quantify all the environmental, radar and target variables, and it is good practice to make rough sketches similar to Figure 4.3 as a check for gross error.

4.7

Limitations of free space formulae

The free space forms of the radar range equation are beguilingly easy to apply. They ignore the environment - factors such as the horizon, precipitation attenuation,

multipath and clutter, which are often imperfectly known. The free space equations are a step to development of more realistic but necessarily more complicated expressions which include these factors. Later chapters show the free space range equations can sometimes understate performance. More importantly, they often very seriously overstate system performance because of environmental effects inseparable from practical marine conditions, particularly at long range. The next chapter starts to consider the way the environment affects echoes.

Chapter 5

Environmental effects on propagation 'The Earth, the air, the sea, the snow; the rain, the fog, the winds that blow.' Anon

5.1

Scope of chapter

The previous chapter looked at a radar and target in unbounded free space. In reality, the space traversed is bounded by the sea surface, which acts as an imperfect mirror. Oblique incident energy is forward-reflected specularly (Chapter 2, Section 2.1.1, Figure 2.1) with an efficiency which depends on surface smoothness. Phase is also shifted at the point of reflection, which is called the grazing point. Arriving via this longer route some nanoseconds later than the direct ray, the indirect rays are delayed in phase as well as being reduced in amplitude. Constructive or destructive interference results from the system geometry and modifies the signal strength at the target. The sea surface follows the curvature of the Earth, introducing a horizon, whose range depends on the heights of the scanner and target, and on the refractive index variation with height of the atmosphere. At long range, multipath interference is replaced by a diffraction mechanism which carries some energy to targets beyond the horizon. Heavy seas may physically obscure or screen the target from time to time, reducing the maximum available probability of detection. This effect is discussed in Chapter 12. The atmosphere is lossy, particularly during precipitation. Near the end of this chapter, we develop the atmospheric loss term L A to account for the attenuation of air, water vapour and precipitation in the radar-target path. The processes recur as the echo returns to the radar. The overall result is usually to reduce detection range so much that performance calculated under free space conditions is hopelessly optimistic. This chapter equips us to develop multipath factors M to describe the differences from free space propagation other than atmospheric loss, in Chapter 6 for point targets and in Chapter 9 for extended targets. Insertion of atmospheric loss and multipath factor convert the radar range equation from free space to real conditions, allowing

echo strength at all ranges to be calculated as accurately as our knowledge of the environmental conditions permits. Precipitation and the sea surface also scatter energy. That returning in the direction of the scanner as unwanted clutter is the subject of Chapter 11. The environmental effects are all dynamic. Movement of hydrometeors in the atmosphere and of sea-waves cause random signal fluctuations, discussed in Chapter 12. In this chapter we consider mean values. Although it is easy to see when the sea is rough or there is precipitation, refraction is normally invisible and its insidious effects are too often ignored. We therefore make no apology for looking at refraction and its effects in close detail in the following two sections.

5.2 Atmospheric refraction 5.2.1 The problem The dielectric constant, £, of a vacuum, such as free space, is defined as 1.0. (This is the relative dielectric constant, relative to the absolute dielectric constant, properly called the electric constant, £o, ^8.854 x 10~12 F/m. (Farads per metre)) The air molecules and water vapour in the atmosphere very slightly increase the dielectric constant, increasing the refractive index, n (n — *J~e) to a value a few hundredths of 1 per cent above 1.0. This very slightly reduces the velocity of propagation from the free-space velocity of light, c, to c/n, reducing the wavelength. If the refractive index were uniform, radar rays would continue to travel in straight lines, just as they do in free space, and the phenomenon would be of trivial importance. However, the rays between marine scanner and target traverse the bottom few tens of metres of the atmosphere. Here temperature and moisture content vary with height, making refractive index also change with height, curving the rays in the vertical plane by an amount dependent on meteorological factors and on range, as indicated in Figure 5. l(a). Refraction therefore affects the ranges at which events such as the horizon occur. At very short range refraction and the associated curvature can usually be ignored, just as Earth curvature is ignored when using plane trigonometry to solve short-range navigational problems. At long range, the relative phasing of direct and indirect rays is very significantly affected, and detection range of distant targets can vary by a factor of two or more as the weather changes from hour to hour. Propagation through the atmosphere is important to radio reception, particularly at the lower frequency broadcast bands and has been closely studied since the 1920s, well pre-dating radar. Air masses are sometimes identified by the thermal and moisture properties of the source region: Antarctic (AA), arctic (A), polar (P) and tropical (T); continental (c) relatively dry, maritime (m) relatively moist. We assume the refractive index, n, of a lamina sheet of atmosphere of constant height /i a above sea level remains constant through the whole scanner/target range bracket. (This usually reasonably represents reality although local inhomogeneities can arise, causing reflection in the form of distributed angel echoes, a form of clutter.) Laminae of differing heights, ha, have differing refractive index.

Air less dense, refractive index, n, low

All curvatures exaggerated

Wavefronts

Slowed by dense air, bottom of wavefronts are retarded, curving ray downwards Direction of propagation normal to fronts Air dense, n high (a) Changing refractive index curves rays

Earth's surface

Source (e.g. scanner)

Direct ray

Rays curved by refraction Low k factor, more curvature

Indirect ray

Destination (e.g. target)

Grazing angle

(b) Curved ray paths Earth true radius, e

Grazing point, specular reflection

Geometric horizon Surface

Scanner

Flat-Earth approximation (dotted) Rays straightened Target Curved rays Effective .surface True surface Earth true radius, e (c) Rays straightened

Figure 5.1

Earth effective radius, E = he

Curvatures unwound

Refraction and ray paths. Dense, moist air near the surface slows the lower portions of the rays, curving them downwards. Path calculations assume straight direct and indirect rays above an Earth whose radius is assumed to be k times actual (c)

As mentioned in Chapter 2, Section 2.4.1, Eq. (2.3), wavelength, A, varies with frequency, / , velocity of propagation, c, and refractive index, n: X= — m.

fn

For a given frequency, raising n from 1 by inserting the atmosphere reduces A., the distance travelled per cycle, hence reducing the velocity of propagation below the free space value. A trivial range error ~300 mm/km arises, much less than other sources of range error such as detection cell quantising, and readily corrected by a small adjustment to the display scaling factor. Much more important than the absolute value of n is its rate of change with height, the refractive gradient, caused by changes of density and moisture content with height. The refractive gradient curves the rays by the same order of magnitude as the curvature of the Earth. At high altitude and over land masses, the refractive gradient is reasonably uniform and unvarying. Unfortunately, within the first few tens of metres above the sea surface, meteorological conditions strongly affect the gradient, in turn varying ray curvature. Neither refractive index nor its gradient is easy to measure. Refraction of course also affects the indirect ray between source and destination and therefore significantly influences the interference between direct and indirect rays.

5.2.2 Equivalent geometries We now quantify these statements. To accord with meteorological usage, some expressions use km rather than metres. In some textbooks, definitions of certain terms differ between km and metres, introducing powers of 103. We let: /za = height of lamina of atmosphere in question, km n = refractive index of this lamina dn/dha = refractive gradient (rate of change of refractive index with respect to height, km) pr = ray curvature, rad/km e = true Earth radius, 6.371 x 106 m £km = e expressed in kilometres, 6371 km E = effective Earth radius k = effective Earth radius factor N = radio refractivity p=barometric pressure, hPa (hectopascal, numerically identical to and superseding the millibar (mbar). 1 hPa = 0.7473 mm of mercury) T = absolute temperature, K w = partial pressure of water vapour, hPa (usually written e, but we prefer w to avoid confusion with dielectric constant and Earth radius). The algebra describing the curved ray paths of Figure 5. l(b) is difficult. It is usual to shorten the odds by an approximation which assumes the rays travel in straight lines above an Earth whose hypothetical radius, E, differs from the true radius, e, by an effective Earth radius factor, Earth radius correction factor or (atmospheric)

refraction factor, k: * = -. (5.1) e This approximation is shown in Figure 5.1(c) (for k ~ 2). The geometry underlying Eq. (5.1) is valid because the ranges and heights used in marine radar are very much less than the Earth's radius. The process is akin to unwinding the curvatures until the ray path is linear. Factor k is a pure number and is independent of radar frequency. However k differs at optical frequencies, which are not affected by moisture. A simpler approximation, discussed more fully in Section 5.6, assumes the Earth is flat and the rays travel in straight lines. This flat-Earth approximation (indicated in Figure 5.1(c)) is tantamount to putting E = oo, with k = oo also. It is valid under some circumstances and we shall use it from time to time, but is inaccurate at long range.

5.2.3 Calculation of refraction factor from meteorological parameters The following treatment is based on Hall etal [1] and on Skolnik [2]. It enables factor k to be calculated in the rather unlikely event that the meteorological parameters in the atmospheric volume traversed by the rays are accurately known. Meteorological measurements taken at a shore station may not reliably apply above the water surface off a coast. Especially near a coast, k may also change along the scanner/target path, vitiating our calculations. As already noted refractive index depends on the dielectric constant: n = y/e.

(5.2a)

For the lower troposphere (the atmosphere up to 11 km), n ~ 1.0003. To magnify the small changes of n which are of interest, we use a radio refractivity, N: 10 6 .

N = (n-l)x

(5.2b)

When, say, n = 1.000315, N = 315, a typical mid-latitude value. Refractivity at the sea surface is sometimes written Ns. The rate of change is also magnified so dha

dha

The value of N depends on the partial pressure of the atmospheric water vapour, w; absolute temperature, T9 and barometric pressure, /?, which are meteorologically inter-related (Reed and Russell [3]): W = 0.373 x 106 ( ^ ) + 77.6 ( ^ ) .

(5.3)

The contribution of water molecules gives the first, 'wet', term, which is usually dominant. Nitrogen and oxygen molecules give the second, 'dry', term. The constants were empirically derived from observations. Except in very calm weather, either the wind or waves make the air turbulent, moisture plucked from the sea surface being

stirred into the bottom few metres of the air column, moistening it. Usually, the following conditions apply. • •

•

•

The air gets drier at height. The rate of change ofp with Aa is negative, p falling exponentially to 35 per cent of the surface value at a scale height, H, around 8 km and not varying much with the weather. The rate of change of T with Aa is negative, except in fog, typically falling at l°/100 m, the dry adiabatic lapse rate. Lapse rate is the magnitude of the decrease of an atmospheric parameter with height. The rate of change with Aa of the wet term is usually, but not always, negative. This governs the gradient dAf/dAa, which in turn governs ray curvature, p r .

Up to Aa > 0.1 km, N usually decreases exponentially; n — nSurface exp(—h/H) and near the surface dn/dha ~ —39.2 x 10~6 km" 1 . The lapse rate —dN/dha often differs from its standard value of 40 'N units'/km (12 'N units'/lOOO ft). The lower parts of wavefronts encounter higher n and propagate more slowly, curving the rays downward as shown in Figure 5.1 (a). Alternatively, we could say that a ray transmitted obliquely upwards encounters decreasing refractive index, making it curve downwards in conformance with Snell's law in optics. The curvature is approximated by

*~ \--wYL ndha] As n ~ 1,

-106

& ~ AAT ,Ai

rad/km.

(5.4b)

From the geometry, Jk = - ^ - . PT

-

(5.5a)

^km

Substituting Eqs (5.4) into Eq. (5.5a) and putting e^m = 6371 km k =

(l+6371drc/d/z a )

=

(1+6.371 x 10~3dA^/dha)'

(5 5

'

)

When dN/dha = —39.2 (sometimes taken as —40), which is approximately the standard lapse rate, k = 4/3. This k value has been adopted for general radio/radar use, giving E = 8495 km. By assuming this fictitious radius, E9 for the Earth, the rays may be regarded as travelling in straight lines in a standard atmosphere, simplifying the ray geometry. Some textbooks use a variant approach. If the Earth is assumed flat, k = oo, a fictitious ray curvature can be adopted to preserve the actual curvature relative to the surface, using fictitious air having a modified refractivity, M as follows: M = N + - x\03 e

= N + 157Aa4N units'.

(5.6a)

Height, hA

Two slope reversals Radar standard

6N/6ha positive Flat Earth Light line

Radio refractivity, N Super-refraction

(a) Standard atmosphere

Figure 5.2

(b) High A: or flat Earth

Sub-refraction (c) Low k

Ducts shaded (d) Surface duct

(e) Elevated duct

Radio refractivity profiles. Idealised, differing weather conditions. Refractive gradient is the reciprocal of the slope of the curves. Not to scale

The 103 term arises from the definition of ha in kilometres. The rate of change with height is the modified refractivity gradient. For the standard atmosphere dM/dha = 117.

a r - ^ + 157dha

0.21, where the algorithm of Eq. (5.41b) has been extrapolated beyond its experimental data.

5.8.6 Values of p The overall reflection (Eq. (5.39)) is plotted in Figure 5.23. It rises from a low value to near unity before gradually being driven down by the divergence factor to zero at the horizon. Peak values would occur nearer the horizon at 9 GHz than in the 3 GHz band shown. When range is less than about 10 per cent of horizon range and sea state is low, vertical polarisation delivers markedly lower forward reflection. Polarisation has less effect at long range where the grazing angle is much below the psuedo-Brewster angle.

5.9 Atmospheric and precipitation losses 5.9.1 Causes of loss Hydrometeors (precipitation and fog particles) in the atmosphere absorb, scatter and attenuate signals, so less energy reaches the target and less still returns as an echo. The

Reflection coefficient, p

Pseudo-Brewster angle

SS5 upwards Dominated by divergence near horizon Vertical polarisation light lines Horizontal polarisation heavy lines

Range, per cent of horizon, log scale

Figure 5.23

Overall forward reflection coefficient, p, variation with range and sea state (SS). Shape of curves somewhat dependent on scanner and target heights. Drawn for these heights each 15 m, k = 4/3. Horizon range 31.9 km. At fairly long range, low sea states and horizontal polarization, p tends to be high

clutter formed by energy scattered on radar bearing is discussed in Chapter 11. The attenuation is dependent on precipitation rate, type and extent, wavelength and, for rain in particular, form of polarisation. Even clear air is not quite lossless; its oxygen and water vapour both absorb a little energy. Each of these losses can be expressed in decibels per kilometre of range bracket through which the phenomenon occurs; the whole path or the range bracket occupied by a rain squall, for example. Atmospheric loss of course reduces clutter as well as target echoes and recurs on the response path. Precipitation rates along the radar/target path are not always uniform or easy to determine, and rates measured at a coastal station may be higher than out at sea, precluding precise assessment of attenuation on any given occasion. The higher precipitation rates tend to occur in squalls occupying only part of the path, introducing less total attenuation. High precipitation rates of course impair optical as well as radar visibility. Although perhaps infrequent, they may pose a disproportionately high navigational hazard, so system performance calculations should be biassed towards the worst case of high whole-path precipitation rates.

Time-distributions of rainfall rates for different areas of the world are available from the ITU.2 Although intended for radio propagation purposes, they may help indicate the likely severity of precipitation loss and clutter on a radar service at a specific location. For example, in the United Kingdom, there is about 0.01 per cent likelihood (~1 h/year) of precipitation exceeding 25 mm/h.

5.9.2 Rain RCS, a, of a single small conducting sphere such as a raindrop, having radius a < 0.1X (in the Rayleigh region, circumference 1 numerically, positive dB), relative to Gmax. Effective gain off-axis = G = - ^ . (2.1 Oc) 8 In free space, when the scanner axis is depressed 8 rad and the target is K rad below the scanner horizontal and so is offset K — 8, gain loss of the direct ray, gK-s, is found by putting v = K — 8 in scanner elevation gain equation (Eq. (2.1Oc)). Effective scanner gain G = G max — gfc-s dB and is used as the gain term in the free-space range equations (Eqs (4.6a), (4.7a) or (4.8a)). Similarly, the indirect ray, inclined at angle rj, has loss gvs. Relative to the direct ray, the differential additional off-axis loss, gdif > almost always approximates 1 and so can be neglected. Its value is gdif =

numerically.

(6.1b)

8r)-8

6.3

Multipath regions

6.3.1 Regions The interference-to-transition and transition-to-diffraction region boundaries are indistinct and rather arbitrary. Figure 6.1 illustrates the vertical lobe structure introduced in Chapter 5, Section 5.6.4, and indicates the regions, which are as follows. 1. Interference region. At short ranges, up to a transition range RA , the signal reaching the destination is modified by interference between the direct and indirect rays. Some authors refer to the transition range as the critical range, but we shall differentiate between these quantities in Section 6.8.1. Ray tracing by geometrical optics as in Chapter 5, Section 5.5, accurately describes operation in the interference region, where we denote the one-way multipath factor of a point target as m p .

(a) Interference pattern above sea surface Upper limit of beam

Lobes Curved up if subrefraction Point target Below horizon

Scanner

Target in second lobe First null. Rays in antiphase-

Not to scale

Target in first lobe. Rays in phase Target path

Free space

Transition range

Actual signal, including multipath Energy on target depends on lobe structure Range, km (b) Signal strength at target

Figure 6.1

Diffraction range

Indirect ray contribution

Interference region

Near Far Transition

Diffraction region

Multipath lobes. As range closes, a point target comes from the diffraction region, through the transition region to the interference region, where it traverses a series of multipath lobes causing signal strength to vary, as shown in (b). Multipath breaks up the relatively wide elevation scanner beam into a number of narrow vertical lobes. Raising scanner height or reducing wavelength increases the number of lobes and depresses the lowest, increasing maximum detection range

2. Diffraction region. When the edge of an object intrudes into the ray path, geometrical optics cannot fully predict what happens. Diffraction of electromagnetic rays around an obstacle can only be accurately described by the mathematics of wave mechanics, beyond the scope of this book. Figure 6.2(a) shows rays striking a conducting obstacle, inducing circulating currents on its surface. Acting as an antenna, the currents re-radiate weakly over a wide arc. Some of the radiation enters the shadow beyond the obstacle, while some modifies the field shortly in advance of it. Alternatively, a plane wavefront can be considered as a system of parallel co-phased wavelets. The obstacle blocks wavelets in its path but oblique radiation from nearby unblocked wavelets penetrates the shadow area, Figure 6.2(Z)), which is based on Hall et al. [I]. The Earth's surface may be thought of either as a collection of obstacles, which together cause some energy to propagate beyond the horizon, or as a moderately conducting sphere on which are induced surface currents extending beyond the horizon, causing local radiation. In practice, unquantifiable anaprop and ducting, described

Incident ray induces surface current which then re-radiates

Advancing wavefronts Wavelets

Rays from radar

Weak radiation diffracts into shadow and modifies incident field Obstacle (a) Induced currents

Figure 6.2

Diffracts into shadow

Obstacle (b) Huygen's wavelets

Diffraction. Alternative elementary mechanisms of diffraction at an obstacle

in Chapter 5, Section 5.2, may mask diffraction effects. When the target or scanner is very low, the diffraction region commences at quite short range, well within the horizon. Surface targets (of zero height) are within the diffraction region at all ranges. With these exceptions, few targets are big enough to remain detectable far into the diffraction region. Some authors [2] recognise only two regions, scattering and diffraction, with their boundary at the radar horizon. On the other hand, it is sometimes convenient to identify near and far sub-regions, etc. as shown in Figure 6.3, with loose boundaries. Figure 6.3 shows variation of multipath factor with range and connects the region boundaries with indirect ray phase shift and attenuation respectively. Drawing to a base of percent horizon range partly generalises the figure for differing scanner and target heights and refraction k factor. Beyond the diffraction boundary range RB, the direct and indirect rays fuse and diffraction is dominant. We denote multipath in this region m&. Although variation of strength in the diffraction region is not truly a multipath effect, there being only one path, it seems convenient to retain the term. Diffraction region calculation is a necessary preliminary for accurate calculation of the following. •

Transition region. As range increases from RA to RB, interference gradually gives way to diffraction. We denote multipath factor in this transition region as m t . No theoretical derivation concisely describes this region. Performance was formerly often defined by drawing, freehand or by French curve, a rather arbitrary smooth curve between the interference and diffraction region graphs. We shall computerise this process.

The multipath factor to be used, M, depends on the region occupied by the target: M = mp, mt or m (right-hand scale)

Phase shift, <j>, rad

Interference region Peaks at almost 6 dB in calm sea (p~l) less if rough ( p « l )

mt Light line. Only valid between RA and /?B Range, % of horizon

Figure 6.3

6.3.2

Interference, transition and diffraction regions. Showing multipath amplitude and phase variations, one-way. Full multipath factor M (heavy line) is the overall multipath factor, changing from mp through Wt to m& as range increases. Note how m p becomes invalid at long range and m&at short range. Path length phase shift 0 governs events in the interference region; falling to n at the horizon, where 0 = Tt. Drawn for: scanner and point target heights 35 and 4 m, or vice versa; sea state 3; k = 4/3; horizon range 32.7km; horizontal polarisation. Per cent horizon range of the events depends somewhat on scanner and target heights, and on radar band, here 9 GHz; at 3 GHz the events occur at shorter range. Theflat-Earth approximation (Section 6.7.2) is indicated. Point Q relates to Figure 6.7

Boundaries

Following Blaise [3], who based his treatment on Kerr [4], we define transition range RA as the range (within the horizon) where indirect ray pathlength total phase shift, 0, is 37r/2rad. Usually, the phase shift at the surface, ty approximates n (Chapter 5, Section 5.8.3, Figure 5.19) so at RA, path length phase shift = TV/2 and — 18dB, while both Meikle [2], and Barton and Leonov [6] prefer 37T/4 and the horizon. Choice of criteria can alter mt by a couple of decibels, ours being the most conservative

RA whenO=37i/4 RB at horizon (Kerr) JRAwhenO=7r/2 A B whenm=-18dB Light line (Meikle)

M, one-way dB

RA when = 7c/2 RA when m=-2OdB Heavy line (Blaise, used in this book)

Range, km

Figure 6.4

Horizon 30.8 km

Effect of boundary changes on mt. For Blaise, Meikle and Kerr boundaries. In this example, boundary differences cause less than 2dB variation in transition region multipath factor

(lowest mt), as shown in Figure 6.4. So performance beyond the interference region is subject to some uncertainty on the score of boundary criteria, any doubts as to how well theory reflects actuality, and of course by the possibility of ducting. For a given radar/target combination, if no range of interest much exceeds RA, it is sufficient to ignore diffraction and assume M falls in a square-law fashion beyond RA, Section 6.8.3.

6.3.3 Transition and diffraction boundary ranges It is often useful to form a quick rough estimate of the boundaries without embarking on detailed calculation. From the flat-Earth approximation, Chapter 5, Section 5.6.1, Eq. (5.27b), when R = RA Air Hh

Tt

0 ~ —~ 2 .-.

RAX *A ~ ^ -

(6.2a)

Doubling scanner or point target height therefore approximately doubles RA- For given heights, RA is three times longer at 9 GHz than at 3 GHz. Some textbooks fail to warn of the error introduced by the flat-Earth approximation within this equation, which under some circumstances predicts RA will exceed horizon range (Chapter 5, Section 5.5.7, Eq. (5.23)), an obvious nonsense. True RA is always less than the flat-Earth approximation. Figures 6.5(a) (3 GHz) and (b) (9 GHz) plot families of an

&=infinity

RA correction factor

(a) 3 GHz band

Approximation

0.001 HhIX , metres, log scale

RA correction factor

(b) 9 GHz band

Approximation (Note change of scaling from Figure 6.5 (a))

0.001 HhIX , metres, log scale

Figure 6.5

Correction for flat-Earth approximation of transition range. Actual (curved-Earth) transition range RA is often much less than the range calculated from Eq. (6.2) for aflat Earth. These correction curves remain approximately valid for all ratios of H to h

RA correction factor to a base of 0.00 IHh/X for differing values of refraction factor k, allowing the Eq. (6.2) flat-Earth value of RA to be approximately corrected for Earth curvature. When k is low and Hh/X is high (exceeding about 500 m) the error becomes gross, true RA falling to a less than a quarter of the Eq. (6.2) value. For example, in a 3 GHz system (X = 0.1 m), scanner height H = 50 m, point target height h = 10 m, Eq. (6.2) gives uncorrected RA = 40000 m and O.OOlHh/X = 5.0. If refraction factor k = 2, the intercept X in Figure 6.5(a) gives correction factor = 0.56 so RA ~ 0.56 x 40000 m = 22.4 km. For the same H9 h and k, in the 9GHz band (X = 0.032 m), uncorrected RA = 125 km but corrected RA ~ 27.9 km. Entry of low scanner and target heights in Eq. (6.2a) shows that RA becomes very low; for example, putting H = h = 1 m in the 3 GHz band gives RA = 0.08 km, all ranges of practical interest lying in the transition or diffraction regions where multipath peaks and nulls do not occur. Our treatment of multipath demands calculation within the interference region as a preliminary to examination of the other regions, so we have to admit it is not well suited to these extreme conditions. Multiplication of the right-hand side of Eq. (6.2a) by a linear approximation [1.87 — 0.435 \og(Hh/X)], shown in Figure 6.5, gives an expression which tends to understate RA-

RA ~ I 15.0-3.48log—1 x — m.

(6.2b)

Figure 6.6 plots the variation of RA, ^ B and horizon range Ru with target height for two representative scanner heights at 3 and 9 GHz, the three panels relating to different k factors. RA typically lies between 0.1 and 0.85 of R^. The slope lines indicate that RA OC h when h is low, migrating towards RA OC /I 4 when h is high; similarly for H. For given H, h and k, RB is of course always higher than RA- When H and h are moderately high, RB is a few per cent above Ru.

6.4

Interference region

6.4.1 Value of multipath factor Reflection of the indirect ray at the sea surface was discussed in Chapter 5, Sectin 5.8. At the grazing point the ray suffers voltage reduction by the reflection coefficient p « l ) of the sea surface, where it is phase shifted by \jr ~ n rad. The path length difference gives an additional range-dependent phase shift . In the following we assume the indirect ray is displaced from the nose of the scanner elevation pattern, so the transmitted indirect my power is reduced by gdif»(^ 1) as discussed in Chapter 2, Section 2.8.1, Eq. (2.10b). The indirect ray voltage component reaching the target, Vind, is less than the direct ray component V^: Vmd = P\/gdtf VdirVind is also subject to total phase shift 0 = and (dashed)"

Horizon, 4 m (dotted) RA, 35 m, 9 GHz band RA, 35 m, 3 GHz band RA, 4 m, 9 GHz band RA, 4 m, 3 GHz band

Target height, h, metres, log scale

Figure 6.6

Continued

Small resultant when rays are near phase opposition

Resultant voltage

Indirect ray

First null Nl

4> = 3n Second null N2 0 = 571

First peak Pl d = 2n Second peak P2

Indirect ray locus Spirals towards P at short range as 0 rises and p falls

Figure 6.7

(f)=4n Direct ray, V^

Vector addition of rays. The resultant voltage OQ varies between maxima when the direct and indirect rays are in phase with (j) = ( U = a 'natural height unit' = 0.5 ( —=J V nl J

L2 = — IE

(6.9)

F(Z) or f(z) is the 'height-gain' function of scanner or target height, respectively, when expressed in natural units of: Z = ^

and

z = ^j

(6.10)

H, h are the scanner and target true heights (m). To give a feel for the quantities, when k = 4/3: £ = 8.49 x 10 6 m, L ~ 13 190 in the 3 GHz band or 9022 in the 9 GHz band. U — 10.24 or 4.8, respectively. Kerr connects Z and z with functions / ( Z ) and f(z) by a graph, Figure 6.8(a). Kerr's Fig. 2-20 was calculated during the Second World War, before availability of computers, for a series solution and an asymptotic expansion, which he does not detail. Particularly as we shall be using a spreadsheet method of calculation, reference to a graph is inconvenient, so we have found an algorithm to represent empirically the height-gain function, graphed in Figure 6.8(Z>), with error in Figure 6.8(c): log[/(Z or z)] = log(Z or z) + 0.001401[2 + log(Z or z)] 6 .

(6.11)

If Z or z < 3, the second term in Eq. (6.11) becomes negligible and log[/(Z or z)] = log(Z or z); Figure 6.8(d). That is, when H and h are low (specifically, when H or

(a) Source data Dots

c) Algorithm error Right-hand scale

(b) Algorithm Heavy line

(d)/(Zorz) = (Zorz) Light line Valid when Z or z< 3

Hor h = 0.1 /0.05/0.03m in Zorz, log scale 3/9/12GHz bands, respectively " HOT h ~ 31 /14/ 10m in 3 / 9 / 12GHz bands

HOT /* = 1025/480/350min 3/9/12 GHz bands

Figure 6.8 Height-gain function. f(Zorz) rises steeply when Z or z > 3. The error curve shows that Eq. (6.11) reasonably matches the curve given in Kerr

h < 31 m or < 14 m in the 3 or 9 GHz bands, respectively), / ( Z or z) ~ (Z or z), as shown on Figure 6.8. Equation (6.7b) connects m^ with R by a bell-shaped curve, when k = 10, minimum useable (H + /z) values at 3.0,9.4 and 14.0 GHz approximate 3.2,1.6 and 1.2 m respectively. To accommodate lower height pairs, the transition range boundary criterion must be reduced, say from —20 to —30 dB. The impact on accuracy is unknown.

6.5.3 Change ofmultipath factor with range Once well into the diffraction region, the exp(—2.02R/L) term dominates Eq. (6.7) and ma falls at a rate determined as follows. Eq. (6.7b) can be expressed in the form R R m& = (constants in a given system) + 10 log 17.55— dB. Li

Ld

At long range R ^> L so R/L ^> log RfL9 permitting the simplification: D

md = constant — 17.55— dB. LJ

Slope = rate of change of m^ with R = dm^/dR. The rule for differentiation of y = axn is dy/dx = anx^n~1^. Rate of change of ma with R = dm^/dR = -17.55/LdB/m. Substituting for L and putting E = ke, ^

= -0.742 x 10- 3 x k'W

x X" 1 / 3 = -0.742^ 2 Z 3 X- 1 / 3 dB/km. (6.12a)

Unusually, this expression is in terms of dB/km rather than dB/decade. Figure 6.9 depicts variation of dm^/dR with k. Eq. (6.12a) is sometimes expressed as - ^ - = - 2 5 7 0 0 ( U V ) ~ 1 / 3 dB/km. dR Note the following. • • • • •

(6.12b)

In the far diffraction region, multipath factor falls at a constant number of dB/km, nearly independent of scanner or target heights (Horh). When H and h are high, the far diffraction region is more distant. When k is low, mj falls most steeply, restricting performance in the diffraction region as well as at short range. The wavelength dependence favours the 3 GHz band. As indicated in Figure 6.3, slopes in the transition and near diffraction regions are somewhat shallower than predicted by Eq. (6.12b) and Figure 6.9.

The total rate of change of echo strength at longest ranges has three major components. •

The free space inverse fourth power relationship of — 12dB/octave (—40 dB/decade). At long range, this gives quite a small rate; for example -0.35 dB/km at 50 km.

dmd / dR, dB / km one-way

Refraction factor, k

Figure 6.9 • •

Slope of multipath factor in far diffraction region

Atmospheric attenuation (Chapter 5, Section 5.9), which only exceeds 0.2 dB/km two-way at short wavelength and in heavy precipitation. 2 drn 3TT/2, Eq. (5.16c)), if R > RB(md < -2OdB),

M = mp (Eq. (6.4));

M = md (Eq. (6.7b));

(6.23)

otherwise M = mt (Eq. (6.15)).

6.7.2 Flat-Earth approximation A flat-Earth approximation is sometimes used, as follows, but introduces significant error so is not recommended. Turning to Chapter 5, Section 5.6.1, Figure 5.12(a), direct ray path length ST is given by solution by Pythagoras's theorem of the rightangle triangle SJT: ST = VFG 2 + SJ2 = y/R2 + (H -h)2.

(6.24a)

The indirect ray path length SZT = SZU is SZT = y W + (FS + GU) 2 = y/R2 + (H + h)2.

(6.24b)

SZT - ST is the path length difference A. Path length phase shift, 4>, is 2n A/A. Assuming perfect phase-inverting reflection at the surface (*!> = JT), although flatEarth multipath factor is not available from a simple equation, it can easily be plotted against range from a straightforward spreadsheet program, giving Figure 6.10 for

Multipath factor, one-way, dB

Interference region, mp Light line Flat-Earth approximation Slope ~ -20 dB/decade Full method Heavy line

//=4m, target height 2 m, 9400MHz, k=4/3, sea state 0, no precipitation Range, km, log scale

Figure 6.10

Horizon 14.1

Multipath factor. Low scanner and target, no clutter. Even under these favourable conditions the flat-Earth approximation overstates performance at long range

a low scanner with a low point target. Accuracy is excellent to RA, somewhat beyond the first peak at 1 km but at longer range the flat-Earth approximation gives signal strengths several decibel too high, the overstatement being 8.6 dB each way at the horizon. When the scanner is high, say 40 m, the flat-Earth approximation is excellent at short range but overstates the first peak range by about 1 km or 10 per cent and signal strength at the horizon is again overstated by ^8.5 dB each way. The flatEarth method settles to a one-way multipath slope of —20 dB/decade at long range, equivalent to echo strength falling 80 dB/decade, 24 dB/octave or R~^. Even at long range, the flat-Earth approximation is much better than use of the interference region multipath factor alone, primarily because the latter's divergence term eliminates the indirect ray at the horizon and forcesrapto 0 dB. Divergence does not occur when there is no surface curvature.

6.8

Two-zone method

6.8.1 General form ofmultipath/range relationship Few systems have sufficient sensitivity to operate into the far transition or diffraction regions. We have seen that at short range, multipath factor fluctuates in value with an amplitude dependent on sea surface reflection coefficient, p, whereas in the near transition region multipath factor falls at about 20 dB/decade. The boundary between these near and far zones is called the transition or critical range, RQ, lying near the transition range, RA- The two-zone approximation to be described enables reasonably quick and accurate calculation of multipath factor to be made into the near transition region but becomes inaccurate at longer range. At short range, average echo strength through a complete multipath cycle follows an R~4 law. Beyond critical range there is an additional R~2 multipath factor each way. The critical range is therefore the range at which the echo power/range law changes from inverse fourth to inverse eighth power. As we shall see in Chapter 9, when targets are extended in height short range multipath fluctuations are muted, and the critical range concept becomes especially useful. We start by examining the rate of change of multipath factor at transition range RA-

6.8.2 Rate of change of multipath factor at RA, calm sea From Eq. (5.16b), 0> = AnH'h'/RX. Substituting in Eq. (6.5a): 9

Tj/'if

mp=4

sin2

dmp

inH'ti

. (6.25a) RX The chain rule for differentiation states that if h(x) = f(g(x)), then h"(x) = fff(g(x))g"(x), where double primes denote the first differential of the functions f(x), g(x) and h(x). Hence, the rate of change ofrapwith R is =

. 2nH'h'

iR -#r

sm

-RT'

,^cl^ (6 25b)

-

At RA, 2nH'h' /Rk = n/2 so the sine term is unity and dmp

inH'ti

R

(625c)

-*i* * = -mx6.8.3 Approximation for multipath factor in near transition region We first assume a calm sea, then a rough sea and finally a moderate sea.

6.8.3.1 Calm sea If there is perfect reflection (p = I9 approximated by calm sea, divergence d assumed unity), by analogy with Eq. (6.25a) the flat-Earth approximation for multipath factor Wfe is

m fe = 10 log (4 sin2 I 7 ^ - 1 J dB. I L RX JJ

(6.26)

When R is small, the expression represents the multipath peak and null structure. From Eq. (6.6), taking the interference region average value of m p (p = 1) to be m p a v = 4(7r — I)/Tt ~ 2.726 = 4.36 dB and ignoring the peaks and nulls gives line AX of Figure 6.11. The relationship changes when the sine term falls to unity at the critical range, so Rc =

2

^ .

(6.27a)

A

Near zone

Far zone

Multipath factor, one-way, dB

X Critical range, calm sea W Critical range, moderate sea Y Critical range, rough sea

Average for full reflection, ignoring peaks and nulls No multipath

Slope -20 dB/decade

Range//?A, log scale

Figure 6.11 Multipath approximations. Interference and near transition regions

Substituting in Eq. (6.2a) (RA ~ SHh/X) for the total reflection condition gives point X: Rc = j KA.

(6.27b)

From this, RA = 4/nRc- This flat-Earth value may be corrected using Figure 6.5. At Rc, mt = mpav = 4.36dB. Above RQ9 InHh/(RX) < 1 so sin [litHh/'(RX)] ~ InHhJRk and here mfe = 4.36 - 20 log — dB

(6.27c)

represented by line XZ. Adding the free space —20 dB/decade term, it follows that when scanner and target effective heights are assumed not to fall as the horizon is approached, echo strength above critical range falls at 80 dB/decade two-way, an /?~ 8 law shown as XZ in Figure 6.12. When the inverse range law is steep, a moderate change in system sensitivity makes little difference to detection range. Rates of change of range with system sensitivity are: R~4 law, 5.9per cent/dB;

/?~ 8 law, 2.9per cent/dB;

R~n law, 1.9percent/dB. 6.8.3.2 Rough sea If there is no surface reflection (p = 0, approximated by rough sea), Wfe ~ 0 dB at short range. Multipath factor can be represented on Figure 6.11 as horizontal line BY

Approximations, calm (upper) and rough seas Heavy lines, -40 dB/decade Moderate sea

Light line intercepting XZ at W (RA) Echo approximation Lies in shaded area, all sea states

Echo, dBW

Critical ranges

Free space+ 8.72 dB Computed, S 52

Perfect surface reflection

Computed, S 55

Free space Zerc surface reflection -40 dB/decade Inaccurate at long range

Point target, 9 GHz band, Sea states 2 and 5, no precipitation

-80 dB/decade Interference region

Near transition region

Range, km, log scale

Figure 6.12

Echo strengths corresponding to Figure 6.11

at OdB, intercepting XZ at Y. Critical range is now IO4-36/20 = 1.65 x Eq. (6.27b) critical range: Rc = 1.65 x -RA

= 13ORA.

(6.28)

Therefore, for a rough sea: If R < Rc (per Eq. (6.28)), mfe = 0, otherwise mfe = 4.36 - 20 log — dB.

(6.29a)

6.8.3.3 Moderate sea Eq. (6.28) shows that critical range rises with sea state and always lies between the limits 0.785 and 1.30 x RA. As 1.0 x RA lies close to their geometric mean, this therefore forms a reasonable average critical range with moderate sea state, justifying the choice of 0 = 37T/2 as the RA criterion in Section 6.3.2, line CWZ representing an average condition. In other words, the transition region commences at the average critical range. Figure 6.12 uses the same notation and shows that CWZ provides a reasonable guide to echo in the interference and near transition regions. The value of W at range RA is 4.36 - 201og4/;r = 2.26 dB. Therefore, CWZ is represented for average conditions by the following. lfR
so it makes sense to raise the latter somewhat beyond that predicted from Eq. (8.6) for the highest radar transmitter power, P, likely to be encountered; radar MDS does not vary much from model to model.

8.4.9 Interaction When two or more racons are operated in proximity, for example, on the deck of a buoy tender before deployment, repeated mutual triggering does not occur should one of them be triggered by receiver noise, another racon or a radar. This is partly because of the combination of low transmitter power, low antenna gain and modest receiver sensitivity; but more particularly because the receiver is purposely inhibited for tens of microseconds after a response transmission. Maximum range at which one racon can trigger another is given by application of a rearrangement of Eq. (8.2a), substituting racon parameters for the 'radar' transmitter and scanner: 201og/? = {/>t + G t - L t } + Gr + 201ogA-201og(47r)-5 r t h s -L A + MidBW. (8.7) Inserting the parameters of the racon of Section 8.4.7, setting L t = L A = 0 and M\ to its maximum value of 6 dB gives R = 35 m as the maximum range at which one such racon can trigger another, assuming no inhibition. Within GEC-Marconi as a routine we operated new racons for 50 h, triggered at lOOOpps from an internal test-pulse generator, before retest to confirm stability of parameters. For convenience, half a dozen might be left running together on the soaktest bench, supply current ammeters indicating triggering activity. Out of curiosity or devilment, on several occasions we tried to get the racons to 'talk among themselves'. They never did.

8.5

User-selectable racons

5.5.7

The problem

The racons described so far have inconveniences. • • •

They can be difficult to perceive in clutter, despite the long response, especially when differentiation (anti-clutter rain) is engaged. Main beam and sidelobe responses continue to display when no longer needed by the operator, distracting attention and possibly masking important targets. Responses are not instantly available on demand but depend on the autonomous muting timer or sweep generator.

Several determined attempts have been made to provide a user-selectable racon service to participating ships while retaining an ordinary non-selectable service for all comers. The systems outlined below have all undergone technically satisfactory sea trials. To prevent inadvertent continual suppression of echoes, they all incorporate spring biassed switches or an equivalent at the radar. In no case has the benefit been deemed sufficient to offset the cost of radar modifications for general use. With the advent of AIS, it seems unlikely that a user selectable racon service will ever be widely adopted.

8.5.2

Fixed frequency and fixed offset frequency

raeons

User-selectable racons responding at band edge and received through a dedicated radar receiver channel were envisaged in the Post War Radar scheme and channels at 2900-2920 and 9300-9320 MHz were reserved for them. Experimental implementation was deferred until the 1970s, by which time the early hoghorn plus cheese squintless scanners had given way to slotted waveguides, whose azimuth beam squints away from boresight in a frequency-dependent manner. Successful trials aboard UK lighthouse tenders with specially modified radars showed that racon, radar and racon plus radar modes could indeed be selected. However, it was realised there would be excessive (> 10 dB) scanner differential squint loss when a transmitter lying near the upper band-edge is coupled to a narrow beamwidth slotted array. Solutions took some years to find. The advent of frequency agile racons in 1980 enabled GEC-Marconi to reduce the loss to less than 2 dB by arranging an agile racon to respond a preset 50 MHz fixed offset from interrogation frequency, e.g. response at 9400 MHz from 9450 MHz interrogation, 9350MHz from 9400MHz, etc. Service to unmodified radars would have been on a time-share basis. Nowadays a lower offset such as 10 MHz would suffice to separate racon and 'radar' (i.e. echo) channels, as in the later USIFAR, Section 8.5.4. Cost of the additional radar receive channel told against the scheme, which never entered service. Performance calculation for fixed offset frequency (FOF) racons is as for user-selectable interrogable frequency agile racons (USIFAR).

8.5.3 ITOFAR Meanwhile interrogation-frequency time offset frequency agile racons (ITOFAR) were developed by L. M. Ericsson as an integral part of their frequency agile Ericon racon development programme under contract to the Swedish Board of Navigation to improve display in clutter, ice clutter being an especial problem in the Baltic. The system has operated successfully in the difficult conditions of the Swedish Archipelago and elsewhere. To ordinary radars, ITOFAR behaves as a standard frequency agile racon already described, where the response immediately follows interrogation and is displayed superimposed on nearby clutter returns. However, co-operating radars can command the racon to delay its response for a preset time, by setting pulse repetition interval to a certain precise value, typically 500.0 |xs. The response then appears in the dead time between interrogations, where clutter returns are negligible. Matching delay

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circuits at the radar superimpose ordinary echoes in correct register on the delayed response. The operator can temporarily suspend the echoes and clutter, the racon response alone remaining at its proper range and bearing for clutter-free scrutiny. The racon trace may also be suppressed when not required, preventing masking of nearby targets.

8.5.4 USIFAR USIFARs are a more recent and neat solution of the offset problem, developed in the late 1990s and offered by Tideland Signal Corporation, Houston, in their SeaBeacon agile racons. USIFARs also serve unmodified radars and are stated to be compatible with ITOFAR. A 3 MHz frequency-modulation is applied to the response of an otherwise standard agile racon. Its interrogation-frequency response component is claimed to fall by less than 1.5 dB, but there are sidebands of comparable power, offset 3 MHz. Ordinary radars accept the first component and operate normally, with a small performance loss. Co-operating radars take the modulation frequency via a separate sharply tuned receiver channel, whose bandwidth may be made narrow, as it only handles long responses, so retaining adequate signal to noise ratio and compensating the reduced power in the sideband. When the operator selects responses alone, they are displayed at the correct location, but with passive echoes and clutter reduced by more than 20 dB. When calculating this racon, noise figure, bandwidth, etc. appropriate to each radar channel must be used, as well as the appropriate response power component.

8.6

Miscellaneous in-band racons

The following descriptions of some other racons and transponders which have been tried and discarded may save the trouble of re-inventing these particular wheels. As far as known none is in current service.

8.6.1 Step-sweep racons The sweep time of conventional slow-sweep racons has to be long enough for at least one, preferably three, scans to lie within the radar receiver bandwidth, limiting sweep rate to about 3 MHz/s maximum, necessitating sweep time of 45 s or more, too long for some short-range applications. Relying on there being eight or more interrogations per scanner beamwidth on the shorter range scales, the 200 MHz of the 9 GHz band is divided into four sub-bands. In absence of an interrogation, the sweep idles in one sub-band, sweeping say 9300-9350MHz at 3 MHz/s, sweep time 16.7 s. The first two interrogations of the scan trigger responses at whatever part of the sweep has been reached, say 9320 MHz. The sweep then steps up 50 MHz to 9370MHz and carries on in the 9350-9400MHz sub-band. The next two responses in the scan are at 9370 MHz. There is another 50 MHz step to 9420 MHz in the third sub-band, and so on. The effect is of a transmitter for each sub-band, each responding

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circuits at the radar superimpose ordinary echoes in correct register on the delayed response. The operator can temporarily suspend the echoes and clutter, the racon response alone remaining at its proper range and bearing for clutter-free scrutiny. The racon trace may also be suppressed when not required, preventing masking of nearby targets.

8.5.4 USIFAR USIFARs are a more recent and neat solution of the offset problem, developed in the late 1990s and offered by Tideland Signal Corporation, Houston, in their SeaBeacon agile racons. USIFARs also serve unmodified radars and are stated to be compatible with ITOFAR. A 3 MHz frequency-modulation is applied to the response of an otherwise standard agile racon. Its interrogation-frequency response component is claimed to fall by less than 1.5 dB, but there are sidebands of comparable power, offset 3 MHz. Ordinary radars accept the first component and operate normally, with a small performance loss. Co-operating radars take the modulation frequency via a separate sharply tuned receiver channel, whose bandwidth may be made narrow, as it only handles long responses, so retaining adequate signal to noise ratio and compensating the reduced power in the sideband. When the operator selects responses alone, they are displayed at the correct location, but with passive echoes and clutter reduced by more than 20 dB. When calculating this racon, noise figure, bandwidth, etc. appropriate to each radar channel must be used, as well as the appropriate response power component.

8.6

Miscellaneous in-band racons

The following descriptions of some other racons and transponders which have been tried and discarded may save the trouble of re-inventing these particular wheels. As far as known none is in current service.

8.6.1 Step-sweep racons The sweep time of conventional slow-sweep racons has to be long enough for at least one, preferably three, scans to lie within the radar receiver bandwidth, limiting sweep rate to about 3 MHz/s maximum, necessitating sweep time of 45 s or more, too long for some short-range applications. Relying on there being eight or more interrogations per scanner beamwidth on the shorter range scales, the 200 MHz of the 9 GHz band is divided into four sub-bands. In absence of an interrogation, the sweep idles in one sub-band, sweeping say 9300-9350MHz at 3 MHz/s, sweep time 16.7 s. The first two interrogations of the scan trigger responses at whatever part of the sweep has been reached, say 9320 MHz. The sweep then steps up 50 MHz to 9370MHz and carries on in the 9350-9400MHz sub-band. The next two responses in the scan are at 9370 MHz. There is another 50 MHz step to 9420 MHz in the third sub-band, and so on. The effect is of a transmitter for each sub-band, each responding

to two interrogations in eight, paired to prevent rejection by radar receivers employing pulse to pulse correlation. There is some loss of paint density on cursive displays, but otherwise the display is almost indistinguishable from a slow-sweep racon, with the benefit of display refresh each 16.7 s. Although generally superseded by agile racons, step sweep might merit consideration where frequent displays are needed at lowest cost. 8.6.2

Fast-sweep

racons

These preceded SARTs (Section 8.8) and work on similar lines. The main differences were that a standard racon coding scheme was used and that the sweep was free running, not starting from band edge when interrogated. Forward sweep rate was ~50 MHz/|xs, with return at 200 MHz/|xs. Response dots displayed at random points within the code envelope, a scan's worth appearing as a speckled Morse response. Fast sweep racons were discontinued because: • • •

sweep loss in narrow band radars was severe, for reasons outlined in 8.2.11; pulse to pulse correlation receivers, which rejected them, came into service; agile racons became available, doing the job better.

Another early fast-sweep racons operated almost exactly like a SART, with sweep as well as response triggered by the interrogation. At least one collision was blamed on confusion between the resulting dot pattern and the echo of an anchored ship. 8.6.3

High power racons

The first racons to go into regular service, already referred to, were primarily intended for long-range landfall and used 9 GHz band magnetron transmitters, duplicated for reliability. The output of about 11 dBW was complemented by receiver sensitivity as high as —95 dBW. The local oscillator of a superheterodyne receiver was tuned to midband. The IF response was flat from 4 to 100 MHz and both sidebands were utilised. The hole in the response between 9396 and 9404MHz was filled by modulating the local oscillator frequency through 8 MHz peak-peak at a quasi-random 1 kHz modulation frequency. Coupled to twin antennas of 7 dB gain, EIRP was some 12 dB more than modern racons. When mounted 75 m above sea level, observed detection range was 60-90 km, extending into the diffraction region. High power racons were made obsolete by the introduction of far cheaper and power-economical solid state devices. Use of radar to make landfall has sharply diminished since introduction of GNSS, but if similar performance were needed today, it would seem better to team a high-gain omnidirectional antenna of narrow elevation beam width with a standard agile racon.

8.7

Cross-band racons and transponders

All the racons described above are in-band devices; the response lying within the 3 or 9 GHz IF band, and automatically painting direct on the display. System bandwidths are inherently wide enough to give good range resolution. In-band racons rely

on the scanner to provide high gain as well as good bearing resolution, necessitating only low power from the response transmitter, an important practical consideration. Radar receivers are unsuited to extraction of much data from the response; more or less limited to a Morse letter, sufficient to distinguish amongst a few racons within an area but little else. 8.7.1

Radar/radio

systems

Radio transmissions have to use narrow bandwidth for spectrum economy and so a radio-frequency response cannot have the sharp edge needed for ranging by pulse methods. On the other hand, walkie-talkie radios show how low (audio) bandwidth depresses noise and permits a data stream (e.g. detailed position messages) to be transmitted at low power between omnidirectional antennas. There are various ways of combining the positioning advantages of radar with the data transmission advantages of radio; radio on one leg with radar on the other, or radar both legs with a supplementary data interrogation or response by radio. Although none has been widely adopted, several have been proposed over the years for the following. • • •

Racon service, but advent of GNSS has lessened the need to transmit data. Ship to ship identification transponders. AIS is intended for this role, but has not yet won full acceptance by the marine community. Carry-aboard transponders reporting ships transiting a waterway, for which AIS now offers a neater solution. Examples include the carry onboard radar transponder (CORT) used at one time by Suez Canal pilots and the Canopus system proposed in the 1970s for the Manchester Ship and Kiel (Nord-Ostsee) Canals.

Detectability calculations follow the same principles as conventional racons. Sometimes similar calculations have to be made at the radio frequency, these follow conventional radio engineering practice.

8.7.2 Radar automatic identification system As an alternative to the IMO-mandated AIS, which is based on GMDSS (the radiofrequency Global Marine Distress Signalling System), and which relies on a navigation satellite constellation such as GPS (Global Positioning System), Midar have put forward their RAIS. This system delivers the radio call-signs of radar targets of interest and is independent of satellites. All vessels and sea-marks such as lighthouses which are to respond as targets would carry an International Standard Interrogation Transponder (ISIT) containing 3 and 9GHz omnidirectional antennas feeding receivers. There would also be a C band (~5 GHz, NATO G band) receiver-transmitter with its own omnidirectional antenna. Antenna gains, azimuth and elevation cover follow racon practice. Ships equipped to interrogate targets would have a similar transponder outfit, linked to their navigation radar(s). The system has been successfully trialled at 5.5 GHz but no operational frequency has been allocated at time of writing. To interrogate a radar echo to find its radio callsign, the operator sets own ship's C band transmitter to fire synchronously with own ship's 3 or 9 GHz radar transmission

pulse when the radar scanner bears on the target. The intended target's transponder only then receives simultaneous pulses, instructing it to respond at C band with a 32-bit digital code of the vessel's Lloyd's Register (LR/IMO) number, unique to the hull irrespective of changes of ownership, flag and callsign. Vessels at other ranges or bearings receive the C band and radar interrogations at different times so remain silent, preventing unwanted responses from interfering, called garbling. C band responses received after a delay matching the range of the echo being interrogated are accepted by the ship. An on-board database, regularly updated, converts the LR/IMO number to the target's current radio callsign, which is displayed adjacent to the radar. The atmospheric attenuation of C band is intermediate between the 3 and 9 GHz band values. The C band interrogation is received inherently free of clutter and the response can be made clutter-free by insertion of a time delay. The C band receiver sensitivity and bandwidth are similar to radar receivers, 40-50 dB more sensitive than racon practice. The C band sub-system uses omnidirectional antennas to avoid the expense of scanners rotating synchronously with the radar scanner. To give range comparable to racons and compatible with VHF ship-ship radio range, the C band response solid-state transmitter delivers of the order of 10 dBW.

8.8

SARTs

8.8.1 Purpose Search and rescue transponders (SARTs) are restricted to the search and rescue (SAR) task of marking vessels and liferafts in distress and are carried by at least a quarter of each roll-on, roll-off (ro-ro) passenger ship's rafts. Electronically, but not operationally, they are akin to swept frequency racons and have similar sensitivity, response power and antenna characteristics, although the sweep regime differs. A supply battery is included within the watertight casing. SARTs are usually deployed on the liferaft mast, inside the non-metallic canopy, constraining mounting height to a metre or so above the water. Trials have established that canopies introduce little loss. Operation is confined to the 9 GHz band. It is the need to operate with SARTs which constrains 9 GHz radars to horizontal polarisation. IMO COMSAR sub-committee's scenario is that the distressed vessel transmits a Mayday message, including position, on the GMDSS system and/or activates an EPIRB beacon whose presence and approximate location are relayed by GNSS satellite to a maritime rescue coordinating centre (MRCC) which alerts nearby shipping, the lifeboat service or SAR helicopters as appropriate. Diaza [2] has reported on operational experience. Life-rafts can be difficult to spot and may drift from the reported position. The SART is intended to mark them on the 9 GHz navigation radar (mandatory on all ships and carried by SAR aircraft) to a range of 5 nmi (~9 km). The SART includes an interrogation indicator, which hopefully prompts the raft coxswain to discharge flares at the right moment. SARTs cannot repeatedly inter-trigger for the same reasons as racons (Section 8.4.9).

8.8.2 Sweep regime Figure 8.15 shows the response process. Although different makes may vary somewhat, typically each interrogation pulse (a) at any frequency in the 9200 (to suit aircraft) to 9500 MHz band generates a single long response pulse (95.4 |xs, b) during which the transmitter frequency, starting at band edge, sweeps rapidly (0.4 JXS forward and 7.5 |xs return) through the whole marine 9 GHz band 12 times (c). Provided the transmitter always sweeps through at least the full band, chirp during the pulse is not too serious; for example, the sweep might be 9200-9550MHz at the start, chirping down 50 MHz to 9150-9500 MHz by the end of the pulse. As SARTs are merely a low power emergency aid, seldom energised, a certain amount of out of band interference is tolerable, which helps reduce cost. 8.8.3

Display on radar

When its scanner bears on the SART, the interrogating radar potentially displays (d) a dot each time the response sweeps through radar frequency. Depending on the location of the radar frequency within the band, the first strong dot may be delayed (Whole process repeats for each interrogation pulse)

(a) Interrogation

(b) Response pulse Full Power

< 0.5 (is delay 12 complete sweeps

(c) Frequency sweep Frequency

Image frequency responses possible Radar receiver passband Wide

(to suit aircraft) 0.4 (is forward, 7.5 (As return (d) Display [First pair

12 pulse pairs

Time, |Xs Forward sweep too brief for full output Short responses, not blanked bv FTC Return sweep, wide bandwidth

Brilliance

Range beyond SART station, km Dot pair interval Quasi-random range offset to first visible dot (e) PPI display

Own ship

Figure 8.15

SART true position

Weak and strong dot pairs

SART bearing

SART timing. Shows effect of radar receiver bandwidth and hence of pulselength

up to 7.5 |xs, painting up to 1.35 km beyond true position (as usual, scaling is at half the speed of light). The first dot is followed by forward and return dots to a total of 12 pairs, spanning a 13 km range bracket; note this is not a measure of detection range. Each interrogation within the scanner beamwidth generates a response group with identical timing; the dots of each response coincide, brightening the dot pattern and avoiding rejection by radars using pulse to pulse correlation. As with swept racons, image frequency reception may occur, displaying an interleaved set of dots. The dots from the quick forward sweep are usually too weak to display and the 12 return dots appear alone. All dots are so short that they are unaffected by the radar FTC facility. SART responses are harder to perceive than the solid lines of racons, especially in clutter, despite the brain's pattern recognition skills, and pose headaches to designers of radar detection systems. Some radars include a dedicated SART mode, in which receiver bandwidth is widened and features such as pulse-pulse correlation are disabled. As with racons, the radar receiver swept gain may suppress the early dots in the response and these may anyway be delayed several microseconds, making the target appear to be at longer range. Navigators may therefore choose to make an oblique approach to reduce the risk of running the liferaft down.

8.8.4 Performance equations - sweep loss Most swept frequency racon performance calculation equations apply. The fast sweep may cause the response to be attenuated within the radar receiver. If the latter's bandwidth is narrow, SART responses (particularly the very quick 0.4 |xs forward sweep) change frequency so fast that the echo is attenuated - the response flashes through radar frequency before the receiver bandpass filter has time to accept it. An alternative viewpoint is that the pulse energy is distributed through a wide spectrum, only a small part lying within the receiver passband. The author learnt this bandwidth problem the hard way long ago when developing a fast sweep racon which worked fine on the test radar but had to be withdrawn from sale after failing miserably in service with radars of narrower bandwidth. Circuit theory predicts that a filter of bandwidth B Hz attenuates sweeping signals by L8 unless the sweep rate Z Hz/s is much less than B2. Filter loss L 8 is somewhat dependent on the shape of the filter response curve but approximates

L s ~101ogf^±Jl) dB.

(8.8a)

In other words, the bandpass filter acts as a single-pole low pass filter, rolling off at 6 dB/octave or 20 dB/decade when the receiver bandwidth is narrow, with 3 dB loss when V z = B. The SART forward sweep has Z = 300MHz per 0.4 |xs so ^Z = / 3 0 0 x 10 6 /(0.4x 10~ 6 )Hz = 27.4MHz and Z = 750MHz/^s. The return sweep takes 7.5 jxs, here \ / Z = 6.4 MHz and Z = 40.6 MHz/|xs. For 1 dB loss,

B = 1.97'Vz.

When Z = 40.6MHz/|xs, B > 12.5 MHz for 1 dB loss.

(8.8b)

Cutoff frequency, return, 6.4MHz

Sweep loss, dB

Cutoff frequency forward, 27.4MHz

(b) Return sweep

(a) Forward sweep

Slopes 20 dB/decade

Receiver bandwidth, MHz, log scale

Figure 8.16

Sweep loss. Radar receiving SART. Approximate; depends on shape of radar receiverpassband. Use wide bandwidth (short range scale/short pulse) to optimise detection of SARTs

Figure 8.16 plots forward and return sweep losses to a base of radar receiver bandwidth, B. On long range scales, many radars have B ~ 2 or 3 MHz, giving forward sweep loss of about 22.8 or 17.3 dB, making the dots difficult to detect. The return sweep suffers 10.5 or 7.4 dB loss respectively. Switching to a shorter range scale using say 15 MHz bandwidth reduces forward sweep loss to 6.4 dB, with return sweep loss 0.7 dB. It is therefore preferable to use a wide bandwidth (i.e. a short range scale) for SART detection, putting up with the additional thermal noise. Wide bandwidth is synonymous with narrow pulselength, which reduces clutter. Unfortunately wide bandwidth is rarely available on the fairly long range scales the operator would initially prefer to use on SAR missions. It has to be said that the sweep times mandated by IMO for SARTs seem rather too fast to accommodate the narrower bandwidths of modern radars. Although really a radar processing loss, it is more convenient to treat Ls as a SART transmitter loss. It is not included within the EIRP. The range equation for the response at the radar is similar to Eq. (8.4a) for a racon, modified by the additional filter loss term:

Sr = [Pt+Gt]-Ls +

G+20\ogX-20\og(47r)-20logR-LT-LA+M2dBW. (8.9)

Relative to a racon of the same receiver sensitivity, response power and antenna gain, SARTs are likely to give inferior performance because: • • •

racons incur less filter loss; racon responses are more readily perceived; racons are usually mounted higher.

The racon curves of Figures 8.11 and 8.12 apply to SARTs except that performance is depressed by the sweep loss.

8.9

Ramarks

A ramark is half a racon, with transmitter but no receiver. Unlike all the other active devices, strictly speaking it is therefore neither a transponder nor a secondary radar. After trialling ramark beacons in 1949, the United Kingdom concluded that racons were preferable. Ramarks have been used (principally in Japan) as aids to navigation, marking buoys and lighthouses. A transmitter generates a steady train of microwave pulses, power ~1 W, spread across a frequency range which usually is a restricted part of the marine 9 GHz band centred on 9375 MHz as favoured by local shipping (not all international radars can participate). Swept-racon-style sweep and muting are included. The radiator is a racon-style antenna. Any nearby radar of suitable frequency accepts the component of energy lying within its receiver bandwidth. Maximum range is typically 10-20 km. The transmission prf is of necessity unrelated to radar prf so response dots are scattered radially across the display at all ranges from zero, building up a fuzzy line on ramark bearing as shown in Chapter 3, Section 3.11, Figure 3.19, accuracy being around 1°, depending on scanner beamwidth. This response feather is on station bearing and extends beyond any clutter which may mask the central portion of the display, so device power can be relatively low. The radar observer can determine position by taking cross-bearings. Many navigators would prefer three lines of position, providing a 'cocked hat' to facilitate error estimation. The LOPs can be provided by other ramarks or conspicuous passive landmarks. As with fast sweep racons, ramark responses are not rejected by fast time constant (FTC) features in the radar receiver. Neither coding nor range information can be extracted. Most modern displays regard such unsynchronised signals as interference from another radar, to be rejected by the pulse to pulse correlation circuit, therefore ramarks have dropped out of use. Detectability can be calculated by treating them as SARTs which are always triggered. Because of the line nature of the response, relatively low single-pulse probability of detection is sufficient.

8.10 8J0J

Radar target enhancers Principle

An RTE, often known as an active reflector, is an electronic device consisting basically of a microwave amplifier connected between small receive and transmit omni directional antennas, intended to enhance the echo of small targets. Received radar pulses are amplified and retransmitted at increased power without significant delay, lengthening or other change. For regulatory reasons, RTE responses cannot be coded and RTEs are not generally regarded as being transponders. The radar displays an artificial echo at RTE position (see Figure 3.19), looking exactly like the echo of a passive reflector target or vessel, but of useful strength and uniform TPM. As with racons, elevation beamwidth can be traded for antenna gain. RTEs are completely inoperative outside their designed frequency band. The electrical power requirement of a few watts is trivial to SOLAS ships and well within the capacity of many yachts.

Figure 8.17

Radar target enhancer. Sea-me 9GHz type. Claimed maximum RCS 63 m2, average 34 m2, meeting ITU-R 1176 and environmental BSEN 90645:1997. Dimensions 416mm x 50 mm diameter, weight 41Og, 12 V power consumption 0.75-3 W. Cockpit display module (right) warns of interrogations. RTEs are widely used to improve RCS of small craft and AtoN buoys. Reproduced by permission ofMunro Engineering Ltd, Wincanton UK

RTEs usually have narrow tubular construction to separate the antennas and prevent self-oscillation, see Figure 8.17. RTEs may be thick on the ground in some marinas, but the similarity of the responses to the yacht passive echoes limits congestion interference. Uptake of RTEs was at first slow, mainly small 9 GHz models for the amateur yacht market. By 2004, many more were being installed worldwide, also finding their way into some offbeat applications - marking remotely controlled jetskis towing gunnery practice targets, for example. Twin-band and 3 GHz models are in development. RTEs are used in the same way as passive reflectors to increase RCS of vessels, offering compactness with a possible cost penalty. RTEs are cheaper than racons so are occasionally used to mark buoys. Interrogations are not 'detected' and reconstituted as with racons and SARTs. Instead, the response pulse is an amplified copy of the interrogation with negligible (nanoseconds) delay, restricting range error to a metre or so. Some yacht-market 9 GHz band RTEs include an indicator of interrogations, warning the skipper to sharpen the lookout as a radar is nearby. This facility does not satisfy the yacht's Colregs duty to maintain an efficient lookout, and should be used

cautiously, because: • • • • •

there is no guarantee that the RTE response is detectable through clutter; the radar range scale in use may not extend to yacht's range; the radar may go unobserved; the ship may be using the 3 GHz band or no radar at all; the RTE may be masked at close range by deck cargo, etc.

8.10.2 Basic description Figure 8.18(a) is a block diagram of a single-channel RTE, usually 9 GHz band, with typical waveforms added (Figures 8.18(b)-(d)). Interrogations are received by a small omnidirectional antenna, usually slant polarised. After a burnout protection circuit, it feeds a microwave amplifier whose bandwidth covers one marine band. As with racons, twin-band devices are essentially separate but may share some components. The amplifier has several stages and overall unsaturated gain, G a , is about 47 dB (9GHz). Bandwidth may not extend to VTS radars using frequencies adjacent to the 9300-9500MHz marine band. The final 'power' amplifier stage is capable of handling a certain rated peak output power Px of the order of 0 dB W or 1.0 W. Suppliers sometimes quote equivalent isotropic radiated power (EIRP), which is Px + G t . In this Receive antenna

Microwave amplifiers total . . Limiter

Protection Interrogation Detector Transmit Antenna G t ~2dBi** **If slant polarised otherwise Gr= Gt ~ 5 dBi (a) Circuit diagram

Video amplifier

Microwave power amplifier /> r ~ OdBW (IW)

Threshold Sths

Supply power

Gate Monostable Warning. Economy or sleep mode Interrogation indicator Optional facilities Response Limit Noise

Small Signal

Threshold not crossed Zero power

Medium Signal

Large Signal (b) Input, point A Stgt

Figure 8.18

(c) Output, point C

(d) Output, with economy mode

RTE block diagram. Typical waveforms are shown. Operation is independent of pulse width. Compared with a racon, Figure 8.7, the RTE is basically a microwave amplifier without detection and regeneration of the microwave signal. Parameters shown give 1OdBm2 RCS

example, EIRP = 2dBW or 1.6 W. A limiter prevents transmitter overload. For purposes of calculation, the overall frequency response of amplifiers plus antennas is usually assumed to remain constant across the band, falling abruptly to zero at band edges. If this is not the case, performance will vary with frequency. A second antenna similar to the receive, but if polarised of opposite slant, transmits the responses. Each antenna is designed as far as possible for omnidirectional response in the azimuth plane and fairly wide elevation beam width to cater for roll; ITU-R Recommendation M. 1176 requires ±15° between half-power (—3dB) points of the pair, much the same as buoy racons. Antennas are sometimes made from an array of three patches printed on a low-loss substrate. Wide beamwidth reduces sensitivity to platform heel at expense of gain and hence of effective RCS, as we shall see. The combined response of the antennas in each plane defines the TPM. As with racons, it is relatively easy to design for smooth TPM. The short feeders connecting the antennas to the amplifiers propagate more slowly than the speed of light, and the signal takes a little time to traverse the amplifier chain. The response is therefore delayed by a few nanoseconds, typically causing less than 1 m range error on the radar display. Although navigationally insignificant, this delay affects the response of RTE/reflector combinations, Section 8.15.4. The great problem of any high-gain amplifier device is self-oscillation, sometimes called ringaround, some of the response finding its way back into the receive antenna and starting a new spurious response - we have all been deafened by howl from publicaddress loudspeakers when the microphone is too close. Oscillation occurs when the gain round the loop exceeds losses. To be precise, vector nett in-phase component of gain in a continuously oscillating loop has to be unity (the Nyquist criterion). In practice the oscillation frequency adjusts itself to meet the phasing condition and the amplitude builds up until saturation reduces nett gain to unity. In a two-antenna RTE the loop is receive antenna, amplifiers, transmit antenna, radiated signal leakage to receive antenna. An oscillating RTE would display as a ramark. The receive/detect/regenerate/inhibit mechanism of racons prevents oscillation and permits their receiver and transmitter to be coupled by a circulator to a common antenna. Even if a leakproof RTE circulator were available, antenna mismatch would reflect enough response into the receiver for oscillation, or there might be reflection from a nearby mast outside the designer's control. The usual solution includes two antennas separated by half a metre or so, slant polarised at opposite hands, with careful radome design to prevent signal creep. Twin band RTEs would almost certainly be taller to accommodate the additional channel. To the receive antenna, responses reflecting once off a nearby mast or other one-bounce object are cross polarised and rejected. A 45° slant polarised antenna will accept any radar polarisation, horizontal, vertical or circular, with loss of half the signal (Section 8.1.9, Table 8.1). Likewise, the radar scanner accepts slant polarised responses as echoes. The resulting polarisation losses of 3 dB each way are included within RTE specifications where appropriate. The difference in antenna heights above sea level makes interrogation and response leg multipath factors M\ and Mj differ slightly, splitting interrogation and response multipath null ranges, so RTEs responses suffer slightly less multipath than point reflector echoes.

RTEs without economy or sleep modes include no detection process, so questions of probability of detection only arise when we come to consider how the radar detects responses in Chapter 12.

8.10.3 Ancillary facilities An optional economy circuit may comprise a detector, video-frequency amplifier, monostable with threshold and gate. When no interrogations are present, thermal noise at the video amplifier output is insufficient to cross the threshold, there is no detector output and the output stage current supply is cut off to conserve power. Any medium-size interrogation pulse from a radar transmitter is detected to give a video pulse which after amplification exceeds the threshold, flipping the monostable for a few microseconds during which the gate is opened for the power stage to respond. Detection may either use a conventional microwave diode as shown in Figure 8.18(a), or may detect the rise in supply current when the power amplifier handles a signal pulse train, cheaper but usually less sensitive. Alternatively, power may be conserved using a sleep mode. If a train of interrogations is received, a slow-acting circuit opens the gate for some seconds so subsequent scans from the radar evoke responses. The auxiliary video amplifier bandwidth may be somewhat restricted to make the RTE less sensitive to narrow pulses to prevent futile responses to interrogations from distant radars using short range scales. As with racon filters, this also reduces sidelobe responses. Calculation of economy and sleep mode sensitivities can be treated along the lines of racon receivers, Section 8.4. Economy circuits also provide a convenient drive to the optional interrogation indicator. Sensitivity of an RTE's optional visual or audible alarm facility is nearly as high as that of a racon receiver, and the alarm will usually be triggered by a distant radar at range well in excess of RTE detection range at the radar. To guard against continuous oscillation, a timeout circuit may briefly interrupt the power supply should the detector indicate a response exceeding about 100 ms.

8.10.4 Specification IMO 's current revision of its specification for shipborne active or passive reflectors, see Chapter 7, Section 7.6.1, may stimulate introduction of more powerful RTEs and spread availability from the 9 GHz band to 3 GHz. Meanwhile RTEs are sometimes tested against relevant clauses of the passive reflector specification, ISO 8729. The draft ITU-R Recommendation for RTEs (ITU-R M. 1176) limits maximum response power to 10 W EIRP (including antenna gains; and presumably to restrict any spurious out of band interference) and tolerates unsaturated RCS at 9 GHz as low as 9 m 2 , which is insufficient for detection in severe clutter. No specification currently addresses the 3 GHz band.

8.10.5 Radar cross section By the inverse square law, halving the range of an unsaturated RTE increases power at its receiver x4. The amplifier delivers x4 response power. The inverse square law

again applies, to give x 16 echo at the radar. As a passive reflector would also give x 16 echo, the unsaturated RTE has a definite RCS. Eventually as range shortens the power stage reaches its rated maximum. The device saturates and no further output increase is possible as interrogation strength rises yet more; this condition occurs with racons at all ranges. RCS now falls as range closes, because response power remains constant, like a racon. Received response power continues to rise, but more slowly. Unfortunately, the term 'saturation' is also sometimes confusingly applied to traffic capacity, the number of responses per second the RTE will support. Because RTEs saturate at short range, may not respond at all at very long range and have vertically separated antennas, no single figure adequately describes their RCS under all conditions. Variation of response at the radar is different from passive reflectors. As RTEs are now replacing reflectors for some tasks, it is interesting to compare predicted performance. To find RCS we consider how response power varies with interrogation strength.

8.10.6 RTE response on axis RTE parameters are quoted inclusive of any internal losses. We adapt the notation and treatment already used for racons: G r , Gt = Receive, transmit antenna gains to signal with same polarisation as radar scanner, dB G a , G 0 = RTE amplifier, overall gains (unsaturated), dB G 0 = G r + G a + Gt

(8.10)

hr,ht = Receive, transmit antenna heights, metres M\, M.2 = Interrogate, response leg multipath factors, dB P r , Pp, Pt = Device response power: rated when saturated, prospective, actually transmitted, dBW AEIR = Transmitted response equivalent isotropic radiated power. PtEiR = Pt + G t , dBW 5 tgt = Signal reaching device per one-way radar range Eqs (4.7a) and (4.7b), dBW Sths = Threshold received signal power dBW, below which device does not respond. May be pulselength-dependent per Figure 8.10, and only applies to RTEs having economy mode ST, SQ = Signal received at radar from active target, echo received at radar from passive object, both per radar range Eqs (4.6a) and (4.6b), dBW If the signal is less than the optional threshold, there is no response. If above threshold (or if there is no threshold circuit, in which case the 'threshold' voltage can be considered zero), the full prospective response power is delivered up to the rated

power limit. Adapting Eq. (8.3): if % < Stfis,

p

t = 0,

otherwise if Pp < Px,

Px = Pp,

otherwise F t = PT-

(8.11)

Assuming the RTE is not inhibited, its received signal, Stgt> is given by radar range Eq. (4.7a) and by the racon equation Eq. (8.4a). Prospective response power P p is raised by the amplifier gain: p p = Stgt + G a dBW.

(8.12)

We consider first the unsaturated condition, followed by saturated. At long range when unsaturated the full prospective response power is delivered: Px = pp per Eq. (8.11), so Eq. (8.12) gives: Stgt = P t - G a dBW.

(8.13)

Substituting for Stgt m Eq. (4.7a), the unsaturated response power is: Px = P + G + G r +201ogA-201og(47r)-201og/?-L t -L A + M i + G a d B W . (8.14) Applying the one way range Eq. (4.8a) for the response leg, the unsaturated echo at the radar is: Sx = Px + Gt + G + 201ogX-201og(47r) - 20log R-LX-LA

+ M2 dBW. (8.15a)

Substituting for Px from Eq. (8.14): Sx = P + 2G + Gx + G a + Gt + 40 log X - 401og(4jr) - 40 log R - Lx - 2L A -LX+

MI+M2

dBW.

(8.15b)

Putting Gx + G a + Gt = G 0 and P + G - Lx = PEIR (at the radar) gives the tidiest version of the response signal at the radar: Sr = PEIR + G + G 0 + 40 log k - 401og(4;r) - 40 log R - L

+ Mi +M2 dBW.

x

-

2LA

(8.15c)

When the RTE is saturated at short range, prospective power exceeds rating and only the latter can be delivered. From Eq. (8.11), Px = Px. Signal at the radar, 5 r , is obtained by substituting Px for Px in Eq. (8.15a) to give an expression identical to that for the racon, Eq. (8.4a): Sx = Px + G + Gx + 20logA,-201og(4;r) - 20log R-LX-LA

+ M2 dBW. (8.16)

8.10.7 Unsaturated RCS Making the approximation M\ + M2 = 2M and rearranging Eq. (8.15c) gives: Sx = PEIR + G + G0 + 20 log X - 10 log(47r) + 20 log X - 30 log(47r) - 40 log R-Lx-

2LA + 2M dBW.

(8.17)

Substituting <JUnsat f° r the bold terms makes the equation identical to the two-way radar range equation for a passive target whose RCS = a unsa t, Eq. (4.6a). The unsaturated RCS of an RTE (which applies at long range and is quoted in datasheets) is therefore the bold terms of Eq. (8.17). Except for substitution of (Mi + M2) for 2Af, to the main beam of the radar, the unsaturated RTE seems indistinguishable from a point reflector whose RCS is (Xunsattfunsat ~ G o + 201ogA-101og(47r) = G a + G r + G t + 2 0 log A - 10.99 dBm 2 , (8.18a) which boils down to: 3 GHz band (X ~ OA m) : a unsat ~ G0 - 31 dB m 2 , 9 GHz band(A - 0.032 m) : a ^ a t - G 0 - 41 dB m 2 .

l

*

}

So to replicate a passive reflector having, say, 20 dB m2 RCS at 9 GHz and 10 dB m2 at 3 GHz, G 0 must be 41 dB at 3 GHz and 61 dB at 9 GHz. IfG1 = Gx = I dB, G a = 37 or 57 dB respectively (Eq. (8.10)). Prevention of self-oscillation with such high gain demands great care during the detailed design phase. The RTE of Figure 8.18 has RCS 1OdBm2. The unsaturated RCS is a property of the RTE alone. Unlike a racon, it is independent of the radar parameters and only depends on range to the small extent that antenna offset makes M\ differ from M2.

8.10.8 Saturated RCS, saturation range At saturation range, RsaX, the amplifier reaches its maximum available (rated) power output. Further halving of range now gives only x4 rather than x 16 echo strength, so effective RCS falls to a quarter. This is the saturation condition, where RCS a (range)2 as with a racon, thus an RTE which is detectable at moderate range may become undetectable when saturated at short range. When saturated, we obtain the response at the radar by substituting Px for Pt in Eq. (8.15a): Sx = Px + Gt + G + 201ogA-201og(47T) - 20 log/? - L r - L A + M2 dBW. (8.19) We find RSSLt by substitution in Eq. (8.14), with P1 = Px: Px = p + G + G r + 201ogA.-201og(47r)-201og /? sat - Lx - LA + M\ + G a .

Therefore 20 log RsaX = P + G + 20 log k - 20 log(47r) - Lt - LA + Mi + G a + G r - P r = Knsat - G t - Pr] + {P + G - Lt} - 101og(47T) - L A + Mx. (8.20a) PrEiR is the response EIRP [PrEiR = P r + G t ] and ftiR is the radar EIRP P H- G - Lx}. We can write Eq. (8.20a) as: 20 log flsat = CTunsat - PrEIR + A reducing Po more than would precipitation clutter of the same mean power. False plots or ARPA tracks may overload the processor enough for it to dump genuine targets. Severe sea clutter is the most important problem facing marine radar designers and dictates choice of several major radar parameters, such as pulse length and scanner aperture. Adding to this, we have seen that sea clutter is vexingly difficult to quantify. Purely statistical treatments do not always fully represent reality and many radar manufacturers prefer to test new designs against their collection of recordings of real sea clutter. It is no light task to compile such a library and it is definitely locked away as valuable 'Company Confidential' intellectual property. Decca Radar, for example, maintained research stations on the tidal River Thames and at Dungeness on the English Channel for many years, making extensive recordings for future analysis, often after a long and frustrating wait for the right weather to arrive. Designs under development could then be tested and refined at will under laboratory conditions against real target and clutter recordings. This attention to detail undoubtedly contributed to the high reputation of their radars. (Decca, now a division of Northropp Grumman Sperry Marine, manufacture the well-known BridgeMaster radars, Chapter 2, Figure 2.2). Clutter at shore stations is not always representative of the open sea, so the author's firm (AEI) preferred to install developmental radars and recorders on a sea-going motor yacht, taking the radar to the clutter. Losing all contact with the trials team after a storm in the Western Approaches, the firm feared the worst. But bad pennies

always turn up and they were snug in the recesses of Swansea Docks, writing up their notes, they said: asleep, we suspected. Datasheets rarely quote specific performance because of the difficulties of effective simulation and the impossibility of turning on a rough sea to order for acceptance tests. Likewise, Type Approval authorities have to take their local sea area as they find it, so cannot test for target detection in clutter, with the result that the IMO radar specifications have had more to say on control knobs than clutter performance, although it is believed a more specific clutter requirement may be introduced soon. In rough seas, the relatively small number of spikes superimposed on the Gaussian element of surface roughness reflect disproportionately large echoes and the tails of the probability distribution become significantly larger than Gaussian. Spikes travel at the speed of the prevailing wind and occupy only a few square metres. If the cell footprint is made smaller, by use of a narrow beam scanner, short pulses or reduced range, the amplitude of the Gaussian component of clutter falls proportionately, the distribution remaining Gaussian. However, all practical radars have detection cells much larger than spike footprints, and the spatial and temporal separation of spikes are so high that there may or may not be a spike within the cell at a given instant. So as cell size is reduced, spike amplitude remains relatively constant and only spike frequency falls. This behaviour, more pronounced with horizontal polarisation than vertical, differs from noise-like precipitation clutter and changes the overall distribution to a 'super-Gaussian' form having higher tails, which, particularly in constant false alarm rate (CFAR) systems, raises the detection threshold and reduces sensitivity. We need a statistical model which enables distribution to be fitted to observed results as sea state changes. Candidates include log-normal and Weibull distributions.

11,73 Log-normal distribution Spikes make the distribution of rough sea roughly approximate log-normal, drawn by re-scaling the abscissa of an ordinary Gaussian (normal) distribution logarithmically. This distribution may raise tail amplitude too far, is not easy to evaluate and does not provide a ready transition which slides seamlessly from the sub-Gaussian distribution describing low sea states as roughness increases. Although we shall not use log-normal distribution, it is detailed in Appendix A2, Section A2.1.

11.7.4 Weibull distribution This distribution has sufficient parameters to allow tailoring to differing tail strengths above or below Gaussian, and is reasonably easy to compute. Since the 1980s, it has been found to approximate observed RCS sea clutter amplitude distributions with considerable accuracy. It can also be used for land and ice clutter, which also have few major scatterers per unit area. The following is based on the full and readable treatment in the earlier part of Sekine and Mao [4]. See Appendix A2, Section A2.5 for additional details. A 1 V rms (normalised) noise signal of Gaussian distribution, after modulation with the local oscillator to become an IF signal, has its negative components folded

over into positive components, changing the distribution to Rayleigh, discussed in more detail in Chapter 12: p(R) = Rexp(-±R2).

(11.17a)

The Weibull distribution of RCS, a, proportional to received clutter power, valid when a > 0, c > 0, and zero otherwise, is p{a)

=

*aQc-\)

exp

(_^1\

(11 17b)

where a is the instantaneous clutter RCS or power, a the scale parameter, here average clutter RCS or power and c the shape parameter, c = 1 for Rayleigh distribution, and is a measure of the degree of organisation of the clutter. Although we shall not do so, because the Eq. (11.17b) form will be more convenient when considering Weibull clutter voltage in Chapter 12, Weibull distribution is often defined with shape parameter rj or C = 2c, so rj = 2 for Rayleigh distribution: p(a) = -a(r]~l) exp ( - — ) . (11.17c) o \ a ) Putting a = 1 in Eq. (11.17b) gives Weibull normalised RCS or power distribution, Figure 11.7: p(a) = 2ca{2c~l) exp(-a 2 c ).

(11.17d)

Integration gives the cumulative probability, Figure 11.8. P(o) = CP = f

p(a) da = 1 - exp(-c 2 c )

(11.18a)

from which

ff = ln

{ [r^]) 1/2C -

(1U8b) High tail increases false alarm rate

Probability, log scale

Shape parameter c = 0.50

Rayleigh Heavy line Smoother Rougher (RCS = 1 m2 rms)

Figure 11.7

Weibull distribution

Instantaneous RCS

Note increased residual probability in rough sec

c= 1.0, Rayleigh (thermal noise and precipitation) c = 0.67, rough sea with sea spikes

(Clutter Im 2 or I W rms)

Figure 11.8

Residual probability

Cumulative probability

Shape parameter c = 1.59, calm sea

Instantaneous clutter RCS or power

Cumulative probability, Weibull distribution

Figure 11.7 shows RCS probabilities for representative values of c. When c is low there is a long tail indicating relatively high probability of the instantaneous RCS (or received clutter power) much exceeding the rms value. The following puts Eq. (11.17a) into Weibull form. It is again normalised with rms a = 1 and is restated in terms of instantaneous voltage, v, where a = v2/2. ( Voltage cumulative probability, CP = 1 — exp I

v2\c I . (1U8C)

Residual probability, RP = 1 - CP = exp ( - — J . Table 11.4 summarises sea clutter parameters quoted by Sekine and Mao from several sources. They report that shape parameter c varies between 0.67 in 'rough sea' and 1.59 in 'smooth sea' where there are many small waves within the detection cell. Assuming that with relatively high definition marine radars at small grazing angles c rises linearly from 0.67 in sea state (SS) 5 to 1.59 at SSO, we suggest that c - 1.59-0.184 x SS.

(11.19)

It is stressed this is the author's supposition only, and it must be remembered that c values also depend in an unquantified manner on detection cell footprint (tending to 1 when footprint area is large), angle of incidence, whether sea or swell, and perhaps on plane of polarisation. Eq. (11.19) indicates that SS3 approximates Rayleigh distribution (c = 1). Lower SS have c > 1, meaning the energy reflected fluctuates less than expected for true noise, with low tail amplitude, presumably caused by wave-to-wave uniformity. For example, a surface resembling a sheet of corrugated

Table 11.4 Sea clutter parameters Wind or sea state

Radar

Wind 10-15 kt 9GHz Wind 30-40 kt 9GHz SS3, into sea K, HP, 0.1 |xs pulse SS3, into sea K, HP, 0.1 ^s pulse SS3, into sea K, HP, 0.1 ^s pulse SS3, into wind L, HP, low res. SS2 9GHz, VP, 40 ns pulse. Cell 31.6 m 2 SS5 9GHz5VP, 40 ns pulse. Cell 31.6 m 2

Sekine and Mao Grazing ref. angle, /3

Shape Median parameter, c RCS/m2

Fig. 2.13b Fig. 2.14 Fig. 2.12

1°

1.24 0.67 1.16

Fig. 2.12

5°

1.65

Fig. 2.12

30°

1.78

Fig. 2.15 Table 2.4

0.5-0.72°

1.585 0.622

-21.4dBm 2

0.495

-16.2dBm 2

Table 2.4

Notes: L band ~ 1 GHz, cell 3 JXS x 1.23°. K band ~ 15 GHz. HP = horizontal polarisation, VP = vertical polarisation.

iron with no high-amplitude events would cause little or no variation of the return as the uniform corrugations slid toward the radar in the breeze and c would be very high. A method of accommodating Weibull clutter distribution will be suggested in Chapter 12, Sections 12.4.2 and 12.4.3.

11.8

Short-range ringing clutter

11.8.1 Feeder ringing Chapter 2, Section 2.6.2, explained how mismatched feeders reflect part of the transmitter pulse back to the receiver before reaching the scanner, perhaps spoiling short-range performance by competing with echoes. When lengthy feeders are employed, ringing can be sufficiently severe to mask quite strong short-range targets and can reduce system performance below IMO minimum requirements. In the following, losses are in decibels. Figure 11.9(a) shows a transceiver connected to a scanner by a feeder, length x metres, ohmic loss F dB/m, so one-way ohmic loss A = Fx. Typical attenuation rates were included in Chapter 2, Section 2.6.2, Table 2.2. For simplicity, the transmitter and scanner are assumed to be equally mismatched; it is straightforward but tedious to extend the argument to differing mismatches or to intermediate mismatches such as a kinked waveguide within the feeder run. As shown diagrammatically at Figure 11.9(Z?), transmissions reach the scanner

Mismatch Feeder Attenuation A=Fx dB, length JC

Mismatch Transceiver

Scanner Transmission loss B (each way)

Transmission loss on receive D Reflection loss E

Reflection loss C

(a) Configuration Transmitter pulse

Radiated main pulse (b) Power flow Main and ghost echoes (at later times)

Ring 1, range 0

Multiple ringing in feeder Radiated ghost pulse

Ghost echo •Main echo Ring 2

(c) Display Rings compete with echo

Ring 3

Etc., giving Ring 3 and higher rings

Figure 11.9 Feeder reflections. Mismatches reflect some transmitter power, which travels to and fro several times before petering out, delivering a ring of false echoes at each pass through feeder attenuation A + transmission loss B. Target echoes are then subject to feeder attenuation A + transmission losses (B + D): loss to echo = 2A + IB + D dB.

(11.2Oa)

The first reflection false-echo ring into the receiver is subject to two-way feeder attenuation, reflection loss C at the scanner mismatch and transmission loss B: loss to first reflection = 2A + C + D dB.

(11.2Ob)

As it reflects at the transmitter mismatch E, again trundles forward along the feeder, is reflected at the scanner and returns into the receiver, each subsequent reflection suffers further loss: loss per ring = E + 2A + C dB.

(11.20c)

Total, second ring (Eq. (11.20b) + Eq. (11.2Oc)) = AA + 2C + D + E dB. (11.2Od) Total loss, nth ring = 2nA + nC + D + (n - Y)E dB.

(11.2Oe)

Scanner voltage standing wave ratio is usually published and transceiver VSWR (> 1) may be winkled out of the supplier if not included in the data sheet. As explained in Chapter 2, Section 2.6.2, losses are found by finding the reflection coefficient of the VSWR from Eq. (2.5a): p = (VSWR - 1)/(VSWR + 1), then substituting in Eqs (2.5b) and (2.5c) to get the mismatch transmission loss (B or D; —10 log (1 — p2) dB) and mismatch reflection loss (C or E; —20 log p dB), respectively, for VSWR of the port in question. Because system timing causes a target at zero range to arrive simultaneously with the first ring, that ring appears as a harmless paint at the display origin (Figure 11.9(c)). Although important to receiver burn-out protection, the first ring therefore does not conflict with targets. The nth ring is displayed as the (n — l)th display circle: apparent range, wth ring =

(tt — I^JCC

GV

m

(11.21)

where c is the velocity of light and GV is the group velocity of the feeder. For coaxial cable, GV ~ f c, ~200m/|xs. For waveguide (Chapter 2, Section 2.6.1, Eq. (2.4b)), GV = c x [1 — (X/2a)2], a being the broad or H-plane dimension. The equivalent echo RCS of the ring, <req, is found by equating it with the echo from a target of the same RCS at the ringing range in question (Eq. (11.21)), using the radar range equation (Chapter 4, Section 4.5.2, Eq. (4.8)). It is sufficient to use the free space form at the short-ranges in question and to ignore all but the feeder-related losses of Eq. (11.20a). target echo SQ =P + 2G + 20 log A - 30 log(4;r) + a - 40 log R - (2 A + IB + D) dBW. Ring 'echo' power = P - (total loss per Eqs (11.20b) to (11.2Oe)) dBW. Equating and re-arranging, a eq = 30 log(4jr) + 40 log R + 2 A + 2B + D - (total loss per Eqs (11.2Ob) to (11.2Oe)) - 2G - 20 log X dBm2. (11.22) Results will be imprecise because no account has been taken of mismatch phasing or the power and time dependence of losses D and E as the receiver protection TR or other device relaxes after the transmitter pulse. Ringing returns are correlated pulse to pulse, so the echo to ring ratio is not improved by pulse to pulse correlation. Echoes coinciding with ring clutter must exceed the latter by fully 1OdB for detection.

11.8.2 Example Suppose a 9 GHz band radar is connected to its scanner via a lengthy waveguide feeder, x = 25 m, F = 0.18 dB/m (waveguide WG16, a = 22.86 mm). At each

port VSWR = 1.5 (representing a moderate mismatch). For the radar: P = 1OkW (40 dBW), G = 30 dBi, X = 0.032 m (9365 MHz). The calculations are as follows. Group velocity (Eq. (2.4b)) = 0.714 c = 214m/|xs. From Eq. (2.5a) p = (1.5 - 1)/(1.5 + 1) = 0.20. Feeder ohmic loss: A = xF = 25 x 0.18 = 4.5 dB one-way. Transmission losses (Eq. (2.5b)), B and D = -101og(l-0.20 2 ) = 0.18dB each. Reflection loss C = E = - 2 0 log0.2 =13.98 dB each. Total loss to echo (Eq. (11.2Oe)) = (2 x 4.5 + 2 x 0.18 + 0.18) = 9.54 dB. Second (first visible) ring occurs (Eq. (11.20)) at R = 25/0.714 = 35 m range. Power of 2nd ring, n = 2 (using Eq. (11.2Oc)) = P - [ 2 n A + nC + D + (n - I)E] dBW = 40 - [4 x 4.5 + 2 x 14 + 0.18 + 14] = -11.18 dBW (0.762 W). Equivalent 2nd ring RCS (Eq. (11.22)), aeq = 33.0 + 40 log 35 + (2 x 4.5 + 2 x0.18 + 0.18) - (4 x 4.5 + 2 x 13.98 + 0.18 + 13.98) - 2 x 30 + 29.90 = 14.09 dBm 2 (25.6m 2 ). Using the same method, the third ring at 70 m has a eq = -10.87 dB m2 (0.082 m 2 ). Because of the assumptions made, these results are not likely to be very accurate. Note how sharply high-order ring RCSs fall in amplitude. The fall would be less if VSWRs were worse. In Chapter 12 we will see that minimum detectable target RCSs need to exceed these ring clutter RCSs by about 1OdB, so only targets exceeding —250 m2 at 35 m or —0.82 m 2 at 70 m are likely to be detected. 11.8.3

Ghost axial echoes

The figure shows that after traversing the feeder three times, a second weak 'ghost' pulse is transmitted. This of course causes a ghost second echo, delayed by the propagation delay in the feeder and causing a ghost paint on target bearing at a distance beyond it of the ring-ring separation. These ghost echoes are not usually noticeable, because only large targets are likely to have sufficient RCS to make them detectable, and the axial extent of such targets may well overlap the ghost. Any further ghosts from the secondary feeder reflections will be weaker still. 11.8.4

Receiver

oscillation

The strong short-range ring signals may induce damped oscillation within the receiver circuits, giving additional rings of interference on the display. This form of clutter is a matter of detail design and is difficult to quantify.

11.9 Man-made interference 11.9.1 Other radars Usually the most troublesome man-made interference received at marine and VTS radars is from other radars - pulsed surveillance radars used for air traffic control and

military purposes, but predominantly those of the VTS and civil marine navigation services, the radars which are the subject of this book. Considering interference from typical shipborne civil marine radar received at a similar radar, pulses received at our radar from the other may be displayed as 'running rabbits' - trains of dots often looking like a ramark responder radial line or like the spokes of a slowly rotating wheel, as indicated in Chapter 3, Section 3.11, Figure 3.19. The other radar may be on own platform (ship or VTS site) or be distant. Its transmissions are of course unsynchronised to ours in prf or scan rate, so its interference paints continuously change in apparent range and bearing and are colloquially called running rabbits. Although not likely to be mistaken for genuine echo plots by an operator or by a plot extractor, the interference is a distracting annoyance and may overload trackformers or ARPA. As an example, suppose each radar has scanner gain 3OdBi, gain to primary sidelobes 2 dBi (28 dB down on main beam) and gain to far sidelobes - 10 dBi through the 360° azimuth. In Chapter 8 we noted that, because only one path leg is in play, a racon having response EIRP of around 6 dBW may be detected to well in excess of 10 km range through the main beam of own radar, the sum of response power and the two antenna main-beam gains, called here the 'leg signal', being ~36 dBW. We first assume both radars operate at the same microwave frequency (or, sometimes, at receiver image frequency). The interfering radar has EIRP typically 70 dBW (e.g. Pt 40 dBW, G 30 dBi), enough to interfere to horizon range or beyond at the comparatively rare occasions when the main beams are on reciprocal bearings with leg signal 100 dBW, say one scan in 180 for 1° beamwidths or eight times per hour, giving severe ramark-like interference on interfering radar's bearing. When one main beam is on a reciprocal bearing to a primary sidelobe, leg signal is 72 dB. When the primary sidelobes are on reciprocal bearings, leg signal is 44 dBW and 'ramark' interference may be experienced to >20km range. Leg signal is 60 dBW when the main beam of either radar scans through secondary sidelobes of the other, giving spoking interference on every scan even when the interfering radar is very distant. When the radars have differing frequencies within the same band, leg signals are reduced by the IF bandpass filter attenuation and interference ranges are reduced. Transmissions in the 3 GHz band are unlikely to be accepted by 9 GHz scanners of the slotted waveguide or VTS reflector scanners fed by waveguide; the 3 GHz frequency will be below waveguide cut-off with evanescent mode attenuation at least several tens of dB/m. But 9 GHz interference can in general be received relatively efficiently by 3 GHz scanners and feeders—depending on detail design—perhaps sufficiently powerfully to cause rectification effects in the receiver, the resulting hiccoughs displaying as echo- or noise-like disturbances. When the interfering radar is on own platform, the scanners must be arranged well outside one another's main beams to prevent receiver burn-out, typically being sited more or less vertically in line. Nevertheless, the scanners couple through far-out elevation sidelobes and through unwanted reflections from nearby objects, the leg signal then being outside the installation designer's control. Transmission should be inhibited within such blind arcs. It is also a straightforward matter to connect transmitter pre-pulses, occurring a few microseconds before transmission, to blank off the

other's receiver, resulting in a pattern of minor blank patches on the display - running rabbit-holes as it were, which are unobtrusive and seldom suppress a third-party echo. If the interference still proves severe, microwave bandstop filters tuned to reject the other radar may be inserted in the feeders, and/or the two radar transmissions may be synchronised. None of these palliatives is available to a distant interferes The usual, and effective, cure for interference is to accept as candidate detections only pairs of echoes occurring within the same range cell, two out of two, a special case of M out of N integration, see Chapter 12, Section 12.6.5.

11.9.2 Own ship Electrical interference sources near the radar may impress unsynchronised noise-like signals onto the receiver, despite its screening and cable filtering. Similar signals may be generated by poor contacts, 'dry joints' caused by faulty soldering, dirty and worn rotating joint sliprings or poor earthing (grounding). The receiver noise factor is degraded, reducing detectability of small echoes, particularly when there is little or no clutter to mask the noise.

11.10 1 2 3 4 5 6

7 8 9

References

CLAPHAM, C : 'The concise Oxford dictionary of mathematics' (Oxford University Press, Oxford, 1996, 2nd edn.) MORCHIN, W.: 'Radar engineers' sourcebook' (Artech House, London, 1993), (cited in MEIKLE, H.: 'Modern radar systems' (Artech House, 2002)) WYLIE, F. J.: 'The use of radar at sea' (Hollis & Carter for the Royal Institute of Navigation, 1978, 5th edn.) SEKJNE, M. and MAO, Y.: 'Weibull radar clutter' (Peter Peregrinus for the IEE, 1990) NATHANSON, F. E.: 'Radar design principles' (McGraw-Hill, New York, 1969), Tables 7-2-7-8 World Meteorological Organisation table, in SKOLNIK, M. L: 'Introduction to radar systems. International student edition' (McGraw-Hill, New York, 1983, 2nd edn.), Figure 13.4 BARTON, D. K.: 'Modern radar systems analysis' (Artech House, London, 1988) FAULKNER, D.: 'Freak waves and survival design', Seaways, The International Journal of the Nautical Institute, 2002 WILLIAMS, P. D. L.: 'Civil marine radar - a fresh look at transmitter spectral control and diversity operation', The Journal ofNavigation, 2002,55, pp. 405-18

Chapter 12

Detection 'There are three kinds of lies - lies, damned lies, and statistics.' Benjamin Disraeli

12.1

Outline

Signal processing leading to target detection was discussed in general terms in Chapter 3, Section 3.6. We now quantify the detection process. Appendix A2 expands on some matters of detail. This chapter, which owes much to expert guidance from Professor E. D. R. Shearman, enables Po to be predicted. Although long, we will only scratch the surface of detection theory. For a taster of the extensive mathematics necessary for rigorous treatment, see for example, Rohan [1], Chapter 3. Theoretical work is ongoing, driven by the needs of telecommunications, and is leading to introduction of refinements in radar data handling software. The next chapter will discuss the errors in measurement and calculation arising from the uncertainties surrounding radar operation.

12.1.1 What we mean by detection Historically, detection was the machine process of extracting radio signals from the carrier, originally using a coherer on the incoming Morse-modulated RF carrier and later by diode rectification or 'demodulation' of the IF. The operator then mentally extracted the Morse or speech data from the residual noise and interference, although machine Morse inkers were soon developed. The rectification process came to be called detection. Radar and radio receivers are similar in some ways, but we use detection in a wider sense, to embrace the whole task of extracting the presence of a target from the surrounding noise and clutter. Demodulation of the IF is one stage of the process and is still sometimes itself confusingly called detection, although we have been careful not to do so. The radar receiver output contains thermal noise, mostly internally generated, and may contain precipitation- and sea-clutter returns, short-range ringing clutter

and echoes from passive or active targets. Detection seeks to maximise echoes and minimise noise and clutter. These latter (except ringing clutter) fluctuate and so do most echoes. Occasionally noise or clutter spikes will be wrongly declared as targets, generating false alarms; correct detections of echoes being irrationally called detections, not true alarms. A decision, right or wrong, that a target is present is a declaration. Sometimes echoes will suffer fades (e.g. from multipath), becoming too weak to be detected. Formerly, most of the detection workload was shared between the integrating phosphor of the long-persistence cursive PPI display and the operator, who decided which paints to accept as echoes and which to ignore as clutter or noise. Nowadays, much of the work is performed by digital software, although the operator still plays a part, optimising control settings and mentally filtering the data presented on the raster display. Detection performance can be predicted by statistical mathematical models of noise, clutter and target fluctuation, idealised to reduce the complexities of the real world to a manageably small number of alternative scenarios or cases. Several differing modelling suites are available. We describe only one - the Swerling Cases, whose predictions have been found to give reasonable accuracy when tried on practical radar/target/environment systems and have proved an essential tool for design of today's radars, with their impressively good detection performance in adverse clutter conditions. The models also give insight to the inherent limits of radar performance and the best control settings for given scenarios. But the models are just that - models - and do not always exactly match reality.

12.1.2 Echo fluctuations Chapters 4-10 developed procedures for calculation of the mean signal strength at the radar receiver from point or extended passive target echoes, and from active device responses (all called 'echoes' in this chapter), applicable to all environmental conditions except ducting. Those chapters explained that echo strength at a given range was often likely to fluctuate, a theme we must now develop. Causes of echo fluctuation include: • • • • • •

target roll, pitch and yaw, which change the RCS presented on radar aspect; roll, pitch and yaw of the ship mounting the radar, which change effective scanner gain; variation of multipath factor from these movements; variation of multipath factor by movement of the sea surface at the grazing point; variation of precipitation attenuation as hydrometeors in the radar/target path randomly fluctuate; noise generated by Feeder ohmic loss.

12.1.3 Noise and clutter fluctuations Chapter 11 discussed the mean strength and fluctuations of competing unwanted returns from the ever-present receiver noise and from precipitation, sea and the

(non-fluctuating) short range ringing clutter components. Fluctuations arise from: • • •

random receiver, feeder and path noise components; the random number of hydrometeors in the detection cell, which randomises the instantaneous precipitation RCS; the random number and height of waves in the detection cell, which randomise instantaneous sea clutter.

We shall express target and noise/clutter fluctuations primarily as amplitude changes, which may occur at various rates: • • •

fast, fluctuating between one pulse and the next (each pulse's return decorrelated from its neighbours); slow, fluctuation being insignificant from pulse to pulse but significant from scan to scan (pulse to pulse correlation but scan to scan decorrelation); very slow, with fluctuation observable only through the period of several scans, with scan to scan as well as pulse to pulse correlation.

12.1.4 Detection in random noise or clutter At given range and multipath, a change in RCS causes a proportional change of echo power, enabling our discussion to interchange freely between RCS and echo power. Echoes have to be detected in presence of noise, precipitation clutter or sea clutter, perhaps all three. To detect is to answer the question 'Does the return within this detection cell contain a target?' Because of the unpredictable fluctuations, an honest observer can only reply between 'Most unlikely', through 'Undecided, need to look for longer' to 'Almost certainly'. Only when the question is qualified to 'Does the return contains a target in excess of an agreed probability of detection while the likelihood that this declaration will be wrong (a false alarm) is less than another agreed value?' can the observer declare a simple and definite 'Yes' or 'No', and then preferably after comparison of the strength of the return in question with its neighbours and with time. 'Yes' might then mean 'more than 50 per cent target likelihood and probability of wrongly declaring Yes with no target present is less than 1 observation event in 10 6 '. In engineering terms, single-pulse probability of detection (PD) > 0.5 (sometimes called 50 per cent), with probability of false alarm (^VA) < 10~~6 (sometimes called 1 in 106, which is really the false alarm rate). There is a definite theoretical limit to the PD available for given PFA, signal to noise-and-clutter ratio, fluctuation type and decision timeframe. A skilled and alert observer viewing an optimally adjusted cursive raw-radar display can sometimes come respectably close to this limit. The observer's decision process can be replicated in a more formal manner by electronic circuits and the powerful digital signal processors of modern radar come very close indeed to the limit, for they can rapidly and untiringly analyse the mass of data generated by the incoming returns and rationalise the comparison process. But the limit is always present. For commercial reasons associated with intellectual property rights, manufacturers are reticent about their detection strategy. This in no way infers they neglect clutter performance when designing radars. On the contrary, designers acknowledge

detection of weak targets in clutter as perhaps their most difficult technical challenge. Living by repeat orders, they must keep up with their competitors to stay in business. Detection performance of radars in service is remarkably good, falling little short of that theoretically possible from published parameters such as scanner beamwidth and receiver bandwidth for any given radar/target/environment system. The inevitable practical shortfall is allowed for by introduction of a processing loss. This term also often includes any shortfall introduced by the operator, who may have quite properly optimised the radar controls for another target lying in a different patch of clutter at different range. Detection, then, is to determine whether a total return event contains a valid signal, using strategies which depend on the properties of noise and other random events described by probability theory, a branch of statistics. Two sorts of error may exist in a declaration: Type I is a false alarm, Type II is missing a target. Both usually have equal importance in data telecommunications work. Because radar final declarations are made only after examination of several sets of data (after several sweeps or scans) and there are relatively far fewer targets than noise events present, relatively more Type I errors are permissible.

12.1.5 Assumptions The relatively slow range-dependent change of returns can be straightforwardly allowed for by re-calculation of the radar range equation and other range-dependent equations developed earlier and can be ignored in the present chapter. If the system noise passes through any form of limiter which clips or reduces high-amplitude events, such as an amplifier lacking sufficient dynamic range, the distribution is broadened, raising PÂ or reducing effective SNR for a constant /VA- Likewise, high-amplitude echoes are reduced, further reducing effective SNR. Therefore in this chapter, unless specifically stated: • • • • •

• • • • • •

range and multipath effects are excluded; ' echoes' refers to responses from active targets, as well as true echoes from passive targets; the sum of signal plus clutter power is called the total return; all amplitudes are referenced to power levels at the input of the radar receiver; echo pulses are assumed rectangular, and where modulated on a carrier, the modulation is assumed sinusoidal with an integral number of cycles within the pulselength, sidestepping tiresome and unrewarding questions of pulse start and finish phasing; we infer actual performance from consideration of what is possible in principle; we normally assume that automatic gain control (AGC) and/or the operator gain control are optimised for the target in question to avoid saturation or cut-off; we shall not consider interference from other radars, which may cause 'running rabbits' on the display; we initially assume that waves do not obscure the target; 'noise' usually means system noise as analysed in Chapter 11, Section 11.2.8, including the scanner and feeder loss contributions as well as receiver noise; we remember that power oc voltage2.

12.1.6 The detection problem Figure 12.1 illustrates the problem of detection in clutter. It shows the digitised returns from a single transmitter pulse on a single bearing, partially filling 500 range cells whose individual capacity is 16 units of power. In (a) the random clutter is modest, the cell counts varying between 1 and 9, average 2.3. This might approximate the areas of light clutter in Chapter 2, Figure 2.6. It is pretty obvious to an observer that the high counts at Q and S represent echo pulses, but opinions might differ how to declare R and T, which in fact are not genuine echoes but particularly high clutter spikes. The next few transmissions within the pulse packet would probably continue to confirm Q and S, not R or T, and might reveal the missed echo at P; but fresh spikes would perhaps cast doubt on some of the other cells. In Figure 12.1(b) the clutter is worse (approximating the heavy clutter areas of Figure 2.6), averaging about 4.4 counts, reducing the signal to clutter ratio.

(a) Low clutter Digitised range cell content

(b) Medium clutter

(c) Echoes

Time, us

Figure 12.1

Signal in clutter: (a) shows that weak echoes can be detected with reasonably high probability in low clutter, but stronger clutter (b) reduces the probability of detection unless a higher probability of false alarms is accepted

Again, the observer can feel sure S is an echo, but may wonder about Q and R, doubt T and have grave reservations on the weak echo P. IfQ is accepted, what about clutter spikes U and V? True echo T is much lower than these and some other clutter spikes. In other words the stronger clutter has reduced the operator's probability of detection of weak pulses and increased the probability of false alarms. The words in italics indicate that detection is never certain. Electronic decision making is subject to similar uncertainties - neither the cleverest person nor the best software can impose certainty when the data is so random. But although an alert operator can make almost optimal detection decisions, electronics does not get bored, drift off into thoughts of that next cup of coffee, break concentration to sign off the Garbage Log, become distracted by radio distress traffic or suffer toothache. Target fluctuations may add to the problems posed by the inherently random nature of clutter and noise. Detection becomes yet more difficult if: • •

•

the echo fluctuates; the clutter is so severe that all the cells are almost completely filled or the preceding receiver is saturated, unable to handle any stronger signal (in the example, count trying to exceed the cell capacity of 16), leaving little headroom for echoes; to exclude clutter, gain has been reduced until the echo barely registers, so that most of the 16 available cells are never used and are wasted.

The total return is a stream of events, most of which represent noise or clutter, perhaps including one or more echoes. Rather than burdening the digital signal processor with many returns so weak they are almost certain to be rejected, a preliminary sorting is usual, based on event amplitude. Only those events having greater amplitude than a certain threshold are accepted as single-pulse detection declaration candidate targets, the remainder being discarded. The signal processor then compares the current single-pulse declaration with the history of activity in that range cell and adjacent cells to deliver the final target declaration to the display. Singly detected pulses are sometimes called blips. The blip/scan ratio is proportional to the number of blips within a scan, so the ratio equals the single-scan probability of detection, and is unity when SNR is so high that all sweeps within the scan deliver a blip. The process is as follows. 1. Make initial decision on each pulse as received, discarding all events which are almost certainly too low to be targets by thresholding, allowing a relatively large number of false alarms in the hope of discarding very few echoes at this stage. 2. Integrate all returns within the scan packet for the range/bearing detection cell in question, correlated echoes accumulating more rapidly than decorrelated noise spikes. 3. Possibly eliminate candidates which, though strong on one scan, are weak on the other (scan to scan correlation). 4. Possibly adapt the decision threshold to the clutter prevailing in the vicinity of the cell location (clutter mapping). 5. Declare all event groups passing this adaptive threshold as plots, to be displayed on the screen.

6. Use ARPA or ATA to form tracks from candidate plot sequences, obtained over numerous scans, which meet acceptance criteria such as maximum rate of turn and acceleration, using the method of plot association.

12.1.7 Rigour Rigorous analysis of fluctuating echoes competing with fluctuating noise or clutter is well beyond the scope of this book, not to mention the author's understanding of statistics. Neither would such analysis yield convenient formulae accurately linking probabilities of detection and of false alarm with signal to noise-plus-clutter ratio (SNR). Beside the primary factors of fluctuation characteristic, SNR and PFA, PD depends to a lesser degree on secondary parameters not published by radar manufacturers, such as the frequency response curve of the radar receiver filter (strictly, its match to transmitted pulse shape). Some practical demodulators have IF-volts-in to baseband-volts-out transfer functions or characteristic curves which change from square law towards linear as signal strength rises. Square and linear approximations yield equations of markedly different form to describe probability of detection; the differences often prove to be more apparent than real, required echoes being within a few tenths of a decibel. Any refinement to PD obtained by inclusion of these factors would be swamped by the practical uncertainties surrounding estimation of target RCS and of clutter intensity. And of course real targets do not always fluctuate in ways which neatly fit the mathematical models used to describe them. Comparison of different textbooks' formulae is bedevilled by differences in definition of signal to noise ratio and some other parameters.

12.1.8 Effect of receiver type After the second demodulator of a superhet receiver, the total video return contains perhaps external noise-like clutter and certainly receiver noise whose bandwidth has been limited by bandpass filters in the receiver IF section. There may be no echo in the return. If the detection system is coherent, the true modulus and phase angle of the original microwave signal are preserved (Chapter 2, Sections 2.2.4 and 2.2.5). The unidirectional baseband pulse and noise then look exactly as though the incoming return had merely been low-pass filtered and linearly rectified immediately on receipt, without any form of distortion (but amplified), in particular the amplitude probability distributions remain unaltered. The video of an ordinary non-coherent receiver also of course contains a demodulated unidirectional echo pulse and noise. In this case the process of mixing down to IF and subsequent demodulation, called envelope detection, discards phase information and changes the probability distribution.

12.1.9 Chapter layout We first consider how a single unidirectional pulse superimposed on a noise background is detected, including some additions to the statistics theory of Chapter 11,

Section 11.3, with formulae for probabilities of false alarms and single-pulse probability of detection; this section is applicable to coherent reception. Non-coherent reception is considered in Section 12.3, catering for the mixing and demodulation processes within most current marine radars where the local oscillator is not phase-locked with the transmitter magnetron. We then account for the fluctuation characteristics of the different cases of target, followed by the improvement obtained by integrating the pulses within a received pulse packet. The chapter ends with several secondary aspects of detection. Appendix A2 contains further remarks on the statistics.

12.2

Direct detection of single pulse in noise

This section assumes unmodulated unidirectional signal pulses and Gaussian noise at the point of detection, applicable to detection systems where either (a) the bandlimited total return is translated down to baseband using a mixer, provided coherence with the signal is maintained, or (b) is directly rectified at microwave frequency. These systems are characterised by an unchanged amplitude distribution of equivalent instantaneous noise power at the antenna and at the point of decision. The section also provides an introduction to Section 12.3, dealing with conventional non-coherent radars.

12.2.1 Detection threshold, unmodulated noise

Instantaneous voltage, R

Suppose the event stream at the point of decision contains only Gaussian noise (discussed in Chapter 11, Section 11.3.8) of long-term voltage Vn rms, instantaneous voltage RVn, fluctuating about a mean of 0 V d.c. According to whether or not the instantaneous noise voltage exceeds a d.c. threshold preset to KVn volts, a noise event may be either wrongly regarded as significant - a false alarm - or correctly discounted as a random spike. The basic circuit is inset in Figure 12.2; in practice

Threshold

A False alarm

B Detected C Not detected

D Detected

Threshold Resistor Narrow-band normalised Gaussian noise (IV rms) Noise

Diode Output Basic circuit

Time (proportional to range)

Figure 12.2 Noise and threshold. Instantaneous noise amplitude detectability of equal superimposed signals B-D

affects

a fast comparator integrated circuit would be preferred. As in Chapter 11, the discussion is simplified by normalising: setting Vn to unity (IV rms) and assuming circuit impedance notionally 1+7*0 ^2 (1 ohm resistive), the threshold becomes K volts, 2.8 V in the figure, which depicts a narrow-band noise specimen similar to Figure 3.4(c). The threshold is crossed when R > K. Such an event, point A, must be a false alarm, for we have said no signal is present; K is called the noise margin, which is really a voltage ratio, referenced to Vn = I V rms. It may also be implicitly referenced to mean noise power and expressed as 20 log K dB, here ~ 9 dB. It is usually easier in practice to reduce the amplifier gain instead of increasing the threshold voltage to adjust noise margin. The effects are identical and are to be understood to apply throughout this chapter. The probability that R exceeds K is the probability of false alarm, also the residual probability, RP (RP = 1 - CP as in Chapter 11, Section 11.3.8). Extending Eq. (11.5e):

PFA = P(R > K) = RP = 1 Fl - erf Cj=)].

(12.1)

Practical false alarm rates are so small, of the order of 10~ 4 -l 0~ 12 , that it is convenient to describe them by F, the exponent of PFA; for example, when PpA = 10~4, F = —4: PFA = 1 0 F , s o F = logPFA.

(12.2a)

The positive quantity — F is sometimes called the false alarm number. The false alarm rate (FAR, number of false alarms per second) is a function of the noise bandwidth, Bn, and the noise margin, as shown in Figure 12.3:

False alarm rate, log scale (alarms/s)

FAR = Bn exp ( - \K2) alarms/s.

Bandwidth

Linear detection system, Eq. (12.2b) Threshold, K, dB above rms noise

Figure 12.3

Variation of false alarm rate with detection threshold

(12.2b)

Gaussian noise, linear detection system (Section 12.2)

(Noise= IV rms)

Figure 12.4

False alarm rate

PFA exponent, F

Threshold K

False alarms/ s per MHz bandwidth

(b) Non-coherent envelope detection at IF Threshold £ Envelope detection in non-coherent radar receiver (Section 12.3). (a) Gaussian noise

Threshold, k or K, V

Variation of PÂ exponent and false alarm rate with threshold voltage

Alternatively, FAR = exp ( - \K2) alarms/s/Hz bandwidth.

(12.2c)

The tolerable FAR is a function of the subsequent machine processing, or of the display tube phosphor and the operator if a simple cursive system is used; its dependence on K is shown in Figure 12.4(a). Having decided that, for example, 1 false alarm per second is permissible and system bandwidth is 1 MHz, Eq. (11.3) indicates that PFA = 1 X 10~6, SO F = — 6. Figure 12.4(a) shows how sharply F varies with K. For F = —6, K must be set to 4.75 (4.75 V d.c. for 1V rms noise, noise margin = 20 log4.75 = 13.5 dB). In Figure 11.2, K = 1.27 (noise margin 2.IdB) gave F = —1 so increasing K by a factor of less than 4 (noise margin change 11.5 dB) reduces PFA by as much as 5 orders of magnitude. Increasing noise margin by another 1 dB from 13.5 dB changes F from —6 to —7.32, reducing /*FA by well over another order of magnitude.

12.2.2 Detection of sinusoidal signal We shall assume the mean noise power remains constant and the signal strength is varied. The bandwidth-limited IF noise envelope is represented by the sum of a pair of mutually independent sine and cosine quadrature carriers whose instantaneous amplitudes are Gaussian about zero mean. An echo event into a coherent demodulator has the form of a burst of sinusoidal IF frequency superimposed on continuouslypresent noise. Figure 12.5, curves (a)-(c), respectively, show the IF noise and signal components and their combination. The noise is normalised Gaussian. The signal at (b) has voltage A = I V peak. The instantaneous voltage of the total return is R, shown at (c). The sine wave rms voltage is A/V2 and the power (into the notional 1 ohm load) is A 2 /2, which we call q times the rms noise power (which is unity).

Thresholds

(a) Gaussian noise, 1V rms

(b) Sinusoidal IF, A = 1V peak

Tx pulselength

(c) Signal + noise R, a = 0.5

(d) IF, A =2 V peak

(e) Signal + noise, a = 2

Vertical grid interval 1V rms Time

Figure 12.5

IF noisy echo pulse. In practice the noise bandwidth would be narrower

Factor q is important and sometimes called the visibility factor or single-pulse SNR. That is A2 SNR = q = — numerically,

(12.3)

so A = */2q. In general, RP is the probability that the threshold is crossed. As a signal is present, crossing now is the probability that the signal is detected, obtained by substituting K-A = K- V2# for R in Eq. (11.4e):

RP = Pn = P(R) = - L exp \~(K

- V7^)2I •

(12.4a)

This expression when graphed has the same form as the probability curve of Figure ll.l(b), unchanged in shape but shifted bodily to the right by A = «Jlq, equivalent to shifting the threshold to the left by A volts. Figure 12.6, curves (a) and (b) are as Figure 11.1 (a) and (b), showing PDF and RP for noise alone. Performance is indicated in the table. Curves (c) and (d) are for a weak signal corresponding to Figure 12.5 curves (a)-(c), while curves (e) and (f) are for a stronger signal, as Figure 12.5 curves (a), (d) and (e). Threshold K1, giving PFA 0.1 (intercept Z l ) intersects weak signal RP at Wl. The strong signal intersect is at S1. Doubling threshold voltage sharply reduces PFA> but drastically cuts PQS. AS SO often, no gain without pain.

12.2.3 Variation of P 0 with SNR Eqs (12.3) and (12.4a) can be used to generate curves of PD versus signal strength for a family of F values using the method of Chapter 11, Section 11.3.8, Eq. (11.5d),

a, b: Noise alone: heavy lines, as Figure 11.1 (a) and(b) c, d: Weak signal + noise, A = 1, q = 0.5 e, f: Stronger signal + noise, A = 2, q = 2

Probability

Residual probabilities

Probabilities of detection

Signal

i

Probabilities of false alarm

(Noise 1V rms)

i

Signal shifts curves to right, shapes unchanged

Probability densities

Thresholds

Instantaneous signal + noise voltage, R

Figure 12.6 Probabilities, signal in noise. Gaussian distribution. Probability density and residual probability curves for noise (as Figure 11.1), noise -f- weak signal (q = 0.5) and noise plus stronger signal (q = 2). Signal shifts PDF and RP to the right without alteration of shape. Low (Kl) and high (K 2) thresholds of detection. Performance as follows Threshold (Noise 1 V rms)

Kl = 1.27 V K2 = 2.54 V

PFA

Zl =0.10 Z2 = 0.0054

PD Weak pulse, q = 0.5 (SdB)

Stronger pulse, q=2 (SdB)

Wl =0.39 W2 = 0.061

Sl = 0.77 S2 = 0.29

giving Figure 12.7. This has been drawn to a primary baseline of signal voltage A, but the noise margin, q dB, is also indicated. Pp is almost zero when SNR = 1 and varies only slowly when Po is near zero or unity, reflecting the wide tails of the probability density function (PDF). When PQ lies between about 0.2 and 0.8, Pp varies almost linearly with signal voltage change at a rate of 0.8 PD units/V peak (0.56 units/V rms). When A = K, PD = 0.5. Here PD would jump abruptly from 0 to 1 if there were no noise. This approximates conditions when swept gain reduces sensitivity at short range. Figure 12.8 presents the curves in a widely used quasi-logarithmic form which better reveals the extreme values of Pp. The ordinate is scaled linearly in terms of D:

D = log M ^ " ] = log PD - log(l - P0).

(12.4b)

P F A exponent, F=-A • Threshold ^=3.71

Heavy line

PD=Q.5vj\&nA=K

(Noise 1V rms) Peak signal volts, A

SNR, q num

Figure 12.7 Variation of Po with signal strength and PFA exponent, linear scaling. Non-fluctuating sinusoidal signal in Gaussian noise. For point R see Section 12.9.2

PD, 'log' scale

D=LOg(P 0 Z(I-P 0 ))

Threshold,/^. (Noise margin)

Figure 12.8

Figure 12.7 redrawn to logarithmic scales

The abscissa is q dB. The thresholds (expressed in threshold to noise ratio, 20 log K dB) for the various PFA have been spotted in. They lie at quite high PDS, because when q = K2, A = V2K and most signal peaks cross the threshold. PD = 0.5 at PFA = 10~6 are typical values needed for effective detection, and require A = 4.7 V, corresponding to voltage strength of 3.33 x noise rms voltage and SNR = 10.4 dB, point T on the figures. Returning to Figure 12.2, equal-sized echo pulses, amplitude K, are shown at B, C and D. Echo B happens to coincide with an instant of zero noise and is just detected. Echo C, at an unfavourable noise instant, is undetectable, while D, at a favourable instant, is readily detected. Several important points can be deduced from the figure and will be confirmed analytically later in the chapter. • • •

Low PpA9 needing high threshold, requires high signal for detection. In noise, low PD can be achieved with weak signals (event D). In noise, high PD requires strong signals (event C would have to be increased to ensure B, C and D were all detected).

12.3

Envelope detection of echo pulse in noise

12.3.1 Detection in non-coherent receiver Ordinary non-coherent receivers (Chapter 2, Section 2.2.1, Figure 2.10(a)) discard the echo phase information component. The receiver input is a microwave echo superimposed on wideband Gaussian noise. The much-simplified block diagram of Figure 12.9 shows how the receiver mixes the noisy signal down to intermediate frequency, where it is amplified as a pulse of sine waves (at say 50 MHz). A filter restricts bandwidth to minimise noise as far as consistent with acceptance of the major frequency components of the signal pulses. Point S is the filter output and is followed by the demodulator, whose output is point T. As the voltage envelope of the IF signal is preserved, this form of demodulation is called envelope detection. A wide-band video amplifier brings thhe output base-band signal to a convenient level for digitisation and subsequent processing, without affecting the mathematics. A voltage comparator (point U) then makes the initial detection decision whenever the instantaneous baseband voltage exceeds the d.c. threshold, again using the basic circuit of the inset in Figure 12.2. Some of these processes upset the conditions we assumed in Section 12.2 and affect the interplay of PFA? PD and SNR. As before, the signal processor then compares the present and previous single-pulse declarations with the history of activity in that and adjacent cells to deliver the final target declaration to the display. The function of an envelope detector is therefore to extract the modulation amplitude while rejecting the carrier, using a demodulating rectifier and a low-pass filter. Modulation by the LO causes the envelope of the bandwidth-limited noise signal at S to be converted from Gaussian to Rayleigh amplitude distribution, see Section 12.3.3. The IF carrier supporting this fluctuating envelope has a fluctuating phase, any phase being equally probable, giving uniform phase distribution.

Narrowbana Threshold, k' IF envelope, Rayleigh Feeder Demodulator Comparator LNA Mixer IF amplifier noise Diode C2. Bandpass Tx pulses filter Wideband IF Video .amplifier Scanner, feeder and first stage introduce Baseband wideband thermal noise Scanner

Target and clutter

M= Microwave frequency Local oscillator Based on Figure 2.10(a)

Figure 12.9

Single pulse declaration Signal Processing Multiple pulse declaration to display

Detection block diagram, superheterodyne receiver

The diode and shunt resistor-capacitor circuit (Rl, Cl) rectify the IF signal and filter out the IF component to yield at T' a unidirectional low-frequency video signal at baseband. It is common practice in marine radar receivers to insert a blocking capacitor C2 after T', so that the waveform at T has zero mean value as shown at (d) in Figure 12.10. We use lower case k for threshold voltage to distinguish from the coherent detection system of Section 12.2. Provided the demodulator diode is 'perfect' (resistance zero when anode voltage is positive to cathode, infinite otherwise), the distribution at its output remains Rayleigh except for a shift in baseline voltage. Figure 12.10 shows a time or range bracket shortly after transmission of a radar pulse. Non-fluctuating echoes el-^9 from different targets are depicted diagrammatically at (a), e\-e7 being equally weak with eS and e9 stronger. Of course, no noise-free waveform of this sort exists; detection would be a doddle if it did! Rayleighdistributed noise (b) combines with the echoes to give a total return as at point S of Figure 12.9. This is shown at (c) after amplification and filtering, with the carrier oscillation at ~50MHz shaded. The envelope outline is rounded by the narrow filter, as expected from Figure 3.4. The demodulator output is the baseband (video) waveform (d). The radar, or the operator viewing a raw-radar display, decides a high event to be a valid candidate echo if it exceeds the threshold voltage. (For raw radar cursive displays, Figure 12.10(d) can be interpreted as brightness, the threshold being the lowest brightness discernible by the operator.) Alternative thresholds k'\ and k!2 are shown applied to the video of Figure 12.10(d) to give alternative comparator outputs (Figure 12.9 point U). In practice, the threshold (or IF gain) would be preset to suit the prevailing noise or clutter. For high threshold k'2, Figure 12.10(e) shows only three noise returns are wrongly accepted to form false alarms ( / ) , so PFA is low. Even so, echoes e\ and e5 are missed (m). On this very limited sample of seven weak echoes, Pn = 5 ~ 0.7.

(a) Echoes. (Unknown to observer) (b) Wide-band noise and clutter

Instantaneous voltage = R volts

Is this event an echo? Equivalent thresholds.

Demoa ulation reproduces envelope contour Alternative high and low thresholds.

(d) Baseband signal after demodulation

(Figure 12.9 point T)

Latency depends on SNR

(e) Declarations, high threshold k'2. (Figure 12.9 point U)

(f) Declarations, low threshold JfI. (Figure 12.9 point U)

Time, us

Figure 12.10

Detection of echoes in noise. Time domain, (d) is the baseband output from the demodulator of a non-coherent receiver. When the comparator threshold is set high (kf2), some echoes are missed (m) but false alarms (f) are few. Reducing threshold to k!\ increases PQ at the expense of poor PPA- Substituting equivalent envelope thresholds kl, k\ simplifies analysis

In an attempt to improve Po, the threshold might be lowered to kf 1. Sure enough, curve (f) shows echo el is now detected, raising P^. But numerous false alarms creep in where there is a noise peak but no echo, raising PÂ- Raw radar would display more noise speckles than echoes. The operator or the machine should compromise by setting the threshold somewhere between kr 1 and k'2, to let through as many false alarms as can be tolerated. The threshold therefore forms a noise floor, the lowest input signal power level that will produce a detectable output signal in the presence of system noise and absence of clutter. As an aside, comparison of (a) and (d) or (e) shows a small but fluctuating time delay or latency between arrival of echoes at the radar and their declaration, caused by the limited system bandwidth. Latency introduces range uncertainty which can cause errors in the historic track of the target and in track prediction, see Chapter 13.

Track-formers therefore require wide bandwidth equating to good SNR (high PD) to produce reliable predictions, see Chapter 13, Section 13.5. 12.3.2 Equivalent envelope detector Inspection of Figure 12.10 suggests identical detection performance would be achieved by declaring detection when the IF envelope exceeds high or low limits k2 or kl, shown in Figure 12.10(c). This concept simplifies the mathematics and gives accurate results provided the system satisfies certain conditions, more or less met by practical radars. • • • •

The initial noise is Gaussian. The demodulator and video amplifier reject the carrier frequency but preserve the IF modulation envelope. Video bandwidth well exceeds half IF bandwidth, so the IF filter defines overall system bandwidth. The circuits have linear transfer characteristics (in practice the demodulator characteristics may permissibly introduce minor non-linearity).

12.3.3 Noise distribution When Gaussian white noise is modulated onto a carrier and passed through an IF filter, the noise output voltage envelope (which cannot be negative and whose instantaneous amplitude is R9 Figure 12.10(c)) takes on Rayleigh probability density function. See also Appendix A2, Section A2.2. The negative components are 'turned over', becoming positive. In general, when the rms value of variable v is a, so that o2 is the variance of v, the Rayleigh PDF is: p(v) = ^ exp ( " ^ 2 )

\V > O].

(12.5a)

When v is a voltage, o is the power in the notional 1 ohm load. Appendix A2, Section A2.2, contains further comments on Rayleigh distribution. In the present instance, if R were a steady peak value of the sinusoidal signal = V2V, the rms value, a, would be 1V, so

p(i?) = 4 e x p [ ~ y . OL

|_

2 Gz J

(12.5b)

The voltage distribution of normalised (a = 1V rms ) Rayleigh-distributed noise is p(R)

= R exp [ - \R2].

(12.5C)

Eq. (12.5c) is shown in Figure 12.11 (a). The whole area under the PDF curve between 0 < R < oo has unit area as usual. The area under the curve to the right of threshold k represents the residual probability (RP = 1 — CP) that the normalised random variable exceeds k. Residual probability is shown at Figure 12.11(b). Any event crossing the threshold is assumed to be an echo. At the moment we are assuming no signal, so crossings must be false alarms. Setting k high reduces

Residual probabilities

a, b: Noise alone: heavy lines, Rayleigh probability (b) RP, noise alone = P FA

c, d: Weak signal + noise, A = l,q = 0.5; Ricean

Probability

e, f: Stronger signal + noise, A = 2,q = 2: Ricean

Probability densities Increasing signal Shapes change Required P FA = 0.1 Threshold set for required P FA

(Noise 1V rms)


Figure 12.11 Ricean probability functions. Noise alone, and signal in noise. At IF frequency in non-coherent receiver. Values ofkl and k2 differ from those used in Figure 12.10. Performance as follows (compare with Figure 12.6) Threshold (Noise 1 Vrms)

KX=IA1SV Kl = 4.30 V

PFA

PD

Zl =0.10 Zl = 0.0032

Weak pulse, q = 0.5 (SdB)

Stronger pulse, q = 2 (+3dB)

Wl =0.22 W2 = 0.0013

Sl = 0.55 S2 = 0.018

false alarm rate but prevents detection of weak echoes. As before, the threshold is therefore set as low as possible, to pass the maximum tolerable number of false alarms. PFA is the probability that the noise exceeds k: POO

P?A = P(R > k) = RP = (1 - C P ) = / = eXP

/

1

RQxpl—R2\

(~^2)-

\

dR (12 6a)

'

Therefore F = log P¥A = log [exp ( - ^ 2 ) ] = -0.217&2,

(12.6b)

k = 2.146V^F.

(12.6c)

so

Say desired PFA is 10 6 . F = —6 so k is set at 2.146 V6 = 5.256 x rms noise voltage. Noise margin is 20 log 5.256 = 14.4 dB. Figure 12.4(b) plots F to a base of £. The curve closely parallels curve (a) for coherent detection, despite the difference in form between Eqs (12.6c) and (12.1). Again F falls sharply as threshold is raised. Raising noise margin by 1 dB so that k = 5.898 shifts F to —7.55 and reduces PFA by 1.5 orders of magnitude. For a given F9 the threshold has to be raised by about half a volt, representing a loss of performance relative to coherent operation. The false alarm rate is a function of threshold and noise bandwidth, follows Figure 12.3 and is similar in form to Eq. (12.2b): False alarm rate = Bn exp ( — ^k2) alarms/s.

(12.6d)

12.3.4 Noisy signal distribution Addition of a signal of amplitude A volts to the normalised noise is accommodated by addition of a term to the Eq. (12.5) Rayleigh PDF, converting the distribution to one introduced by Rice [2] and discussed in Appendix A2, Section A2.3. Ricean distribution is a more generalised development of Rayleigh. PDF of the modulated noisy signal voltage is p(R) = RI0(RA) exp [ - \(R2 + A2)].

(12.7)

I0 (RA) is the modified Bessel function of zero order (already discussed in the context of sea forward reflection in Chapter 5, Section 5.8.4, with approximation Eq. (5.4Ie) and Figure 5.21). When A = 0, I0 (RA) = 1 and the expression reverts to Rayleigh, Eq. (12.5c). Figure 12.11, curves (c) and (e) show the PDF curve departs from the Rayleigh curve (a) and changes shape as signal strength increases. The left skirt remains tied to the origin while the peak slumps downward to the right, the area under the curve of course remaining unity. CP and RP change shape in sympathy with the PDF. The RP curves (d) and (f) are reversed-S shaped from 1 at the origin. PD is the probability that R will exceed k and is the area under the PDF to the right of A:. The threshold for PFA = 0.1 is 2.12, higher than for unmodulated noise (k = 1.27). The weak signal now has PD = 0.22 but the strong signal Po is 0.55, which is acceptable for many conditions. Doubling threshold to 4.24 reduces Po more than for Gaussian probability: weak signal Po becomes very low at 0.0013, strong signal PD = 0.017, far too small for reliable detection. For the same PFA-> Ricean Po s are lower than Gaussian because the phase component of information has been discarded. PD is found by substituting from Eq. (12.7) and then Eq. (5.4Ie): Po=

P(R) d R=

= I00 R(l +l!Â))

RI0(RA)QXp

\--(R

2

+ A2) I d R

exp(^) exp [-!(«2 + ^ ) I a.

(12.8)

This expression is difficult to evaluate. Approximate solutions are included in the next section and Appendix A2, Section A2.4.

P FA exponent F=-4

Heavy line

Envelope detection

Single pulse SNR, q, numerical

Figure 12.12

Single pulse probability of detection, non-fluctuating signal. Linear scales, differing from Figure 12.7

Figure 12.12 graphs single-scan PQ to a base of q for representative values of F. The curves are rescaled logarithmically in Figure 12.13. Comparing with Figures 12.7 and 12.8, the families of curves are similar despite the apparent differences in the underlying equations, Bessel function and all. Non-coherence introduces some loss. Within the important region where F lies between —4 and —8 with P& between 0.1 and 0.9, this necessitates an increase in q of about 0.8 dB, which of course is included within Eq. (12.8). The thresholds again lie at high PpS, in excess of 0.95. When rms signal = threshold, peak signal voltage is V2 or 3 dB above threshold and only occasionally does an unfavourable noise spike in phase opposition depress the resultant enough to prevent detection. It was noted in Chapter 11, Section 11.3.9, that atmospheric and feeder noise make the echo noisier. The effect is small and may be treated as an increase in the receiver noise background rather than as an echo component. 12.3.5 Approximations for PD calculation

Eq. (12.8) is unfriendly, but help is at hand. Levanon [3] offers a remarkably simple approximation: q = a + 0A2ab -\-l.lb numerical

where:

a=\j°ji\ \PFAJ

and

fo=lnr_î. LI-PDI

(12 .9)

PD, 'log' scale

Threshold, k

Heavy line

Single pulse SNR, q, dB

Figure 12.13

Figure 12.12 redrawn to logarithmic scales, which better depict extreme values of Po- Threshold indicated for each PFA

Converting to common logarithms and rearranging gives forms directly connecting single pulse SNR (q, numerical), PFA exponent F, and Pp in the form D = 1Og[ZVd - PD)I as Eq. (12.4b): q = (3.783 - 0.636F)D - 0.4780 - 2.303 F numerical.

(12.10a)

To be meaningful, q must be positive, setting an F-dependent bound to lowest usable PQ: PD

> 0.07 (F = - 3 ) , > 0.04 (F = - 4 ) , > 0.019 (F = - 6 ) , > 0.010 (F = - 8 ) , > 0.006 (F = -10), > 0.005 (F = - 1 2 ) .

Rearranging,

and Po =

T

10 D T T ^ .

(12.10c)

Figure 12.14 compares Levanon's approximation with PQS calculated per Eq. (12.8) for F = —3, —6 and —12. Accuracy is good to at least PD = 0.99, with no unpleasant surprises at intermediate Fs. Unfortunately, Pp is overstated at low q; error exceeds 1 dB at PDS of 0.46, 0.19 and 0.14 respectively.

PD, 'log' scale

PFAexponent F = —3

Solid lines: Accurate expression Dotted lines: Levanon's approximation Dashed lines: Levanon modified, C = 1/3

Single pulse SNR, q, dB

Figure 12.14 Approximations for Pp of single pulse. Non-fluctuating target. Levanon s and modified Levanon s approximations compared with Figure 12.13 The understatement is almost eliminated by addition of a correction term to Eq. (12.10b), shown bold in the following expression: _ D =

(q+ 0.4780 + 2.303 F) x (1 - CF/q) 3.783-0.636F '

(12

-Ua)

An alternative correction term [1 + F2/(3q2)] would give even less error but determination of q for given Po and F would embroil us in solution of a cubic equation. Choosing constant C relatively low gives only partial correction at low Po but minimises error at high PD. Taking C = \ seems to offer a good compromise and is compared with Levanon and the accurate expression of Eq. (12.8) in Figure 12.14, error being shown in Figure 12.15. In these figures, q is shown in decibel form. Given F and Po, q can be found by extracting the positive root of a quadratic equation q2 + sq H-1 = 0, so q = I [ — s + v s2 — 4t] numerical, where s = D(0.636F - 3.783) + F(C H- 2.303) H- 0.478,

t = CF(2303F + 0.478).

(12.11b)

Maximum when PD ~ 0.85 (all F s )

P n error

Pn errors

PD values in italics

Graticules 0.01 P n unit

Minimum when PD -0.33 (all Fs)

Figure 12.15 Accuracy of modified Levanon approximation. The approximation (Eq. (12.11a), C = ^) differs from the accurate expression of Eq. (12.8) by less than ±0.025, errors being worst when PD ~ 0.33 or 0.85 A real solution requires s2 > At, for which PD must exceed the following values, which although higher than for the Levanon approximation, are below PDS commonly used for main-beam detection but not for sidelobe detection, restricting the usefulness of the modified Levanon approximation: P 0 > 0.24 (F = - 4 ) ;

> 0.18 (F = - 6 ) ;

> 0.15 (F = - 8 ) ;

> 0.13 (F = -10); > 0.12 (F = -12). When q and PD (hence C) are given, PFA exponent, F, is found in a similar manner by taking the positive root: F=

-s' + Js'2 - Ar't' 2P

where / = 2.303,

/0.478 \ s' = I + 1JC + 0.636D + 2.303 f' = 0.478+ 4-3.783ZX

(12 llc)

'

12.3.6 Accuracy Figure 12.15 indicates the error in determination of PD from the modified Levanon approximation Eq. (12.11a) rather than from Eq. (12.8). PD numerical error has been plotted to a base of q for several representative PpA exponents, F. The error in PD is always less than ±0.025. When PD per Eq. (12.11a) M).33 the error is maximum negative and actual PD ~ 0.35. When PD ~ 0.85, error is maximum positive and actual PD ~ 0.83. Error is negligible when PD is very low, very high or near 0.55. Other sources of error include the following. • • • •

Noise bandwidth may differ from signal bandwidth. The radar does not actually perform detection at IF but at video. Second-order effects in the radar are not reflected in the mathematical modelling. Demodulator transfer characteristic. Square-law demodulation is rather better in weak signals but linear is better when the signal is strong. Luckily, the nominally linear demodulators commonly used become somewhat square-law to weak signals, so our assumption of envelope demodulation of the IF waveform usually introduces less than 0.2 dB error.

12.4

Single pulse detection in clutter

12.4.1 Noise and precipitation clutter In non-coherent systems, calculation of detection in precipitation clutter is exactly as for detection in noise because they share the same distribution, initially Gaussian. Clutter power (W, not dBW) is merely added to the noise power in the equations. Signal to (noise plus clutter) power ratio can directly replace numerical signal to noise ratio in the equations for detection in noise, explaining why signal to noiseplus-clutter ratio is so often abbreviated to SNR. To retain the desired PFA in clutter, threshold k has to be raised to prevent declaration of clutter returns as targets. This reduces PD and explains why clutter inevitably impairs target detectability, even when a clever signal processing system keeps the display screen clear. The PDF is as Figure 12.11 and Eq. (12.5b) of Section 12.3.3, when the receiver is non-coherent, otherwise Figure 12.6 and Eq. (12.4a) of Section 12.3.3 apply.

12.4.2 Clutter with Weibull distribution Chapter 11, Section 11.7.4, showed that sea clutter may approximate Weibull distribution with shape parameter c. Land and ice clutters also approximate this distribution. The following puts Eq. (12.5a) into Weibull form to align with Eq. (11.18). It is normalised by putting a = 1 and restated in terms of instantaneous voltage, v, where a = V1Il. Voltage CP = 1 - exp (

J .

Residual probability, RP = 1 - CP = exp / - — J .

PFA exponent, F

Rayleigh, c= 1.00 Heavy line

(Clutter voltage 1V rms)

Figure 12.16

Voltage, v

Variation of PFA exponent with threshold voltage for a range of Weibull shape parameters. Sea states tentative. The Rayleigh curve for noise or precipitation clutter follows Figure 12.4 (a), whose axes had different scales

Using subscript c to indicate conditions at shape parameter c and setting threshold kc at the value of v which gives RP equal to the desired PFA having exponent Fc:

10êxp[-f], so

Fc = logexp [ - ^ j = -0.4343 ^ J

(12.12a)

and kc = - V 2 X ( 2 . 3 0 3 F C )

1/(2C)

.

(12.12b)

Substitution of Eq. (11.19) (which tentatively links c with sea state) into Eq. (12.12a) links F with v and sea state as shown in Figure 12.16. Figure 12.17 shows demodulated noise waveforms for different shape parameters.

12.4.3 Equivalent sea, land and ice clutter Detection circuits can be devised to assess shape parameter and optimise detection tactics to suit, say, a rise in sea state but it is doubtful whether they are used in the civil marine field. Usually, it suffices to assume that the threshold of a conventional detector is merely adjusted to maintain the desired false alarm rate, the threshold

(a) Shape parameter c= 0.67

(b) c= 1.0 (Rayleigh)

All signals 1 V rms Time

Figure 12.17

Demodulated noise waveforms. Weibull shape parameters c = 0.67 (rough sea), c = 1.0 (Rayleigh) and c = 1.59 (smooth sea). Signal is demodulated so voltage is unidirectional. Higher c describes less spiky clutter

rising as the shape parameter falls, also of course rising to accommodate the higher rms voltage. We tentatively suggest accounting for non-Rayleigh shape parameters caused by sea spikes etc. (Chapter 11, Section 11.7.2) by re-scaling the clutter voltage using a clutter weighting factor W (power by factor W2) to give the same effect as Rayleigh distribution. Suppose Rayleigh normalised noise or clutter is received and the desired P$A is 10~6, F = —6. In accordance with Eq. (12.6c), the appropriate threshold is k = 5.257 V, point A on Figure 12.16. Ifnow the clutter is thought for argument's sake to remain 1V rms but changes to sea state 5, c = 0.67, Eq. (12.12b) shows that k has to be increased to 10.04 V, point B on the figure, increasing by a voltage factor W = 10.04/5.257 = 1.91, preventing the increased number of high spikes from generating extra false alarms. Reduction of the rms clutter voltage to 1/1.91 = 0.52 V rms (by 5.68 dB, point X on Figure 12.18) would restore F to —6 at k = 5.257. In other words, sea clutter of voltage v and shape parameter c can be treated as Rayleigh clutter, c = l , of voltage Wv or of power (Wv)2. The value of W depends on F and c and is found as follows, where subscripts c and 1 denote Weibull and Rayleigh conditions, respectively. For Weibull noise, from Eq. (12.12a) - F c = 0.4343 ( | - )

(12.13a)

Clutter weighting factor, W, dB

SS5? Weibull shape parameter c = 0.67

P ssumes shape parameter varies linearly with sea state F FA exponent, F

Figure 12.18

Variation of Weibull clutter weighting factor with PFA cm d sea state. Applicable to small detection cells

and for Rayleigh noise, c = 1

-F 1 =0.4343 №Y IfFi =Fcmdkc

= Wki c

0.4343 {\k\) Wlc

= 0.4343(£fcJ).

Therefore

(\k\)c-lW2c = \ and W = (\k\fc-l)/2c]. Substituting for k\ W = (-2.303Fi ) [ ( 1 " c ) / 2 c ] numerically or W = 20 I —-]

log(-2.303FO = 10 j —-]

^ ( - 2 . 3 0 3 F 1 ) dB. (12.13b)

Figure 12.18 shows the variation of W as FpA exponent F is varied, for the family of shape factors tentatively linked to sea states. We see that SS 5 clutter boxes about 5.6 dB above its weight when F = —6, whereas calm-sea clutter is several dB more

False alarm exponent, F = -12

Clutter weighting factor, W, dB

(heavy line)

Applies to all forms of clutter Shape parameter, c

Figure 12.19

Variation of Weibull clutter weighting factor with shape coefficient. Applies to all forms of clutter

benign than expected from its RCS. W approaches OdB at high PFA and always remains nearly OdB at SS3. When the sea area within the detection cell is large (at long range, long pulses, wide azimuth beamwidth), W approaches OdB. As no allowance has been made for this unqualified dependence, Eq. (12.13b) exaggerates W under these conditions. Figure 12.19 is redrawn to plot W to a base of c for a family of typical F values and may also be used to weight land and ice clutter having Weibull distribution. It shows the false alarm exponent only weakly affects W within the usual working range where — 4 > F > —12. When there are two or more clutter/noise sources, perhaps noise and sea clutter, having different shape parameters, it is probably sufficient to apply the appropriate W factor to each source and then add their powers (W, not dB) to give the resultant noise/clutter.

12.5

Target fluctuation

12.5.1 The problem So far this chapter has concentrated on a single echo pulse, assumed the target has definite fixed RCS so its echo is non-fluctuating with fixed power, and explained probabilities of detection based on the echo power relative to the mean of the fluctuating noise plus clutter. Without noise or clutter, non-fluctuating echoes marginally below threshold would never be detected but echoes marginally above threshold would have

PD = 1.0. The target RCS or echo power probability density function (PDF) would be a narrow spike of great (theoretically infinite) height enclosing unit area, coinciding with a cumulative probability (CP) step function from 0 to 1.0. Only noise and clutter would introduce uncertainty to spoil the picture. At very short range, noise and clutter may be small and the threshold is then set via the swept gain function to reject trivially small echoes from birds and so forth. The CP here does approximate a step function. And a few real-life longer-range 'hard' targets, such as reflectors and racons, discussed later, do indeed have nearly constant echo strength. But, as indicated in Chapter 7, Section 7.10, for point target pairs and Chapter 10 for extended targets, echo strength of most targets fluctuates significantly above and below their means. We avoid the term Fades, which might infer reductions only, fade margin then being the echo in hand above that required to achieve the required PDIt is not essential here for us to dissect which of the fluctuations listed in Section 12.1.2 change target RCS and which modulate the path loss of the direct/indirect ray combination at the radar receiver. It is enough to regard fluctuations interchangeably as variations either of echo power or of target RCS, whichever is convenient, about the mean values considered in previous chapters. Even without noise or clutter, it is impossible to be sure whether a single observation of a fluctuating target shows it above or below its mean strength. Even when mean echo is below threshold, there remains some probability that a particularly strong pulse will exceed threshold and be detected; or a weak pulse from a generally strong target may fail to cross the threshold. Fluctuation therefore broadens the echo PDF from a spike to a hump. The curve of probability that return exceeds threshold, P (R > k), changes from a step to a rounded curve, the area under the curve of course remaining unity. Any receiver noise (or clutter) fluctuations compound the detection uncertainty. An above-average echo may sit on a low noise (or clutter) event to preclude detection, or a belowaverage echo may coincide with a high noise event to enhance detectability. Noise and clutter are of course unaffected by target fluctuation so the threshold remains as before, Eqs (12.6c) or (12.12b).

12.5.2 Swerling fluctuation cases Target fluctuations differ so widely that before attempting calculations of PD some simplifications or abstractions have to be made, by allocating targets to a few broad representative classes or cases which can be mathematically modelled. We choose to use one of the oldest models, proposed by Swerling [4], which has stood the test of time and is still widely used in detection studies. It was briefly mentioned in Chapter 7, Section 7.10.6. Swerling's famous cases include three distributions of observed RCS (or echo) values. • •

Case 0. RCS does not fluctuate. Cases 1 and 2. Targets with many (theoretically an infinite number, but in practice exceeding 4 or 5) independent scatterers of approximately equal strength,

•

no one scatterer predominating; targets whose width or height are very many wavelengths. RCS has Rayleigh probability distribution. Cases 3 and 4. Targets with one dominant plus several subsidiary scatterers, or a single non-uniform scatterer subject to modest changes in viewing angle. Cases 1 and 3 are distinguished from Cases 2 and 4 by the rate of change of RCS.

•

Cases 1 and 3. RCS fluctuates on a time scale slower than the scan interval (~2 s), so returns on adjacent scans are uncorrelated and provide independent samples of instantaneous RCS. However, returns within a single scan are correlated so may not average the long-term mean; for example, the returns in a scan may be all low or all high. Case 3 is subdivided.

• •

Case 3a. Case 3 target viewed by single radar in the ordinary way. Case 3b. Case 1 target viewed by a decorrelated pair of dual-diversity radars, adequately separated in frequency or position.

•

Cases 2 and 4. RCS effectively uncorrelated between adjacent pulses (~1 ms apart) and therefore also uncorrelated scan to scan. For a single pulse, performance approximates Case 1 but when 10 or more pulses are integrated (Section 12.6.4), detectability approaches that of Case 3a. Case 2 applies to frequency agile radars, possibly occasionally used in VTS service, and perhaps to helicopter and small hovercraft blade flash echoes. Case 4 targets are rare in marine practice and will not be discussed further. All cases. RCS remains constant for the pulse duration of ~ 1 |xs.

•

The cases are at best only approximations to reality, so detectabilities calculated with their aid will include error, adding to imprecisions in knowledge of average target RCS, actual radar parameters, environmental conditions on the day and so on. That said, the Swerling Cases offer a good footing for comparison of likely detectability of differing radar/target/environment systems. Table 12.1 summarises them and Figure 12.20 shows their probability distributions. If a target's case is unknown it is prudent to be pessimistic and assume Case 1, whose instantaneous RCS lies below the average oftener than above, necessitating higher average RCS than Case 0 or Case 3 targets to get high PD-

12.5.3 Case 0 (Case 5) non-fluctuating target Also called Swerling Case 5, the Marcum Case or a hard target. All echoes are identical in strength, equalling the mean. We have partially analysed this case in the previous sections. Echoes have full or perfect pulse-to-pulse and scan-to-scan correlation, meaning each sample size is related (here equal) to its neighbours rather than being random. There is unity probability that the echo power is the average value. The PDF is therefore a spike or delta function centred on average RCS, enclosing unit area, at the point where CP steps from 0 to 1, see Figure 12.20. Figure 12.13 indicates that, even in noise, quite a small RCS or echo strength increase raises Po from 0.10 to 0.90: for example, 4.2 dB when PpA = 10" 6 .

Table 12.1

Targetfluctuation;Swerling Cases 2

3a

3b

4

Correlated Uncorrelated Slow Many independent scatterers Ships and all physically large targets Ricean, Eq. (12.14a)

Uncorrelated Uncorrelated Fast Many independent scatterers Freq agile radar, helo blade flash Eq. (12.16a)

Correlated Uncorrelated Slow One dominant plus other smaller scatterers Buoy, small yacht, buoy + racon? RTE + yacht? Eq. (12.17a)

Correlated Uncorrelated Slow Dual diversity radars

Uncorrelated Uncorrelated Fast As Case 3a

Oorl

Eq. (12.14b)

Eq. (12.16b)

Eq. (12.17b)

Eqs (12.7a), (12.8), (12.11a)

Eq. (12.15c)

Eq. (12.16c)

Eq. (12.18c)

8.8 dB

7.OdB

-7.OdB

7.5 dB

5.9 dB

13.OdB

21.2 dB

-21.2 dB

17.3 dB

15.7 dB

4.2 dB

14.2 dB

-14.2 dB

9.8 dB

9.8 dB

Swerling Case

0 (or 5)

Pulse to pulse Scan to scan Fluctuation Target characteristics

Correlated Correlated Non-fluctuating Single reflector with large solid angle Good point reflector, racon or RTE alone Line

Typical marine targets Target alone: probability distribution Target alone: cumulative probability Target in noise: probability of detection Single-pulse SNR,

Case 1 target

Eq. (12.21a)

Eq. (12.21b)

Eq. (12.22f)

PD0.1,PFA10- 6

Single-pulse SNR, P0 0.9, PFA 10"6 Change, P0 0.1-0.9

Note: Quoted equations and SNRs apply to detection by non-coherent radar receiver.

None

To infinity

PDF, Case 0. Spike of zero width and infinite height, enclosing unit area.

CP, Case 0, (step change) CP, Case 1, heavy line Probability

CP, Case 3a

CP = cumulative probability PDF = probability density function Total area under PDF curve = 1.0 for each case

(Mean RCS or power = 1 unit rms, o = 1)

Figure 12.20

Instantaneous RCS or echo power

Probability distributions, Swerling Cases. Normalised. Case O nonfluctuating targets are represented by a spike. When the signal is strong, Case 1 has lowest cumulative probability, the integral of probability density. Case 3 is intermediate between Cases O and 1

Targets approximating Swerling Case 0 include the following. • • • •

Terrain echoes without moving foliage, particular when seen by a groundfast radar. Radar interrogations at racons and racon responses at radars, Section 12.9. Platforms (particularly when groundfast) carrying radar reflectors or RTEs whose RCS exceeds skin RCS by 20 dB or more. Targets such as octahedral reflectors having target pattern maps whose RCS changes slowly with angle are best treated as non-fluctuating with RCS equal to the device mean, or, more prudently, the minimum RCS sustained through an angle of 10° (IMO's 'stated performance level' for reflectors, see Chapter 7, Section 7.6.1).

12.5.4 Fluctuating targets Figure 12.21, based on Figure 12.11 for Ricean distribution, illustrates diagrammatically how the uncertainty of signal strength creates uncertainty of residual probability (equivalent to Pu), which may lie between strong and weak instantaneous RCS points S and W. If the fluctuation is slow, as for most marine targets (Cases 1 and 3), the echo might remain above average for a whole scan, whereas quick fluctuation (Cases 2 and 4) would enable a reasonable estimate of Pp to be formed from the packet of

Probability of detection

Noise + lower likely limit of signal Noise + higher likely limit of signal Residual probability lies within shaded area Probability of detection fluctuates Noise alone

Required P FA Threshold set for required P FA

Figure 12.21


Probability of detection, fluctuating signal Signal fluctuation adds uncertainty to the curves. FQ of a pulse mayfluctuate between points S and W

echoes within the scan. So both the spread of instantaneous echo strengths about the mean, and fluctuation rate, must be considered, forming the reason for differentiating between Cases 1, 2 and 3. No two targets fluctuate in quite the same way, and the fluctuations of a given target may change with sea conditions, for example, increasing roll or yaw. Noise associated with the two-way attenuation of atmospheric, scanner or feeder loss modulates the echo and introduces a component of fluctuation, biasing the Swerling Case from Case 0, etc., part-way towards Case 2. This effect, partially rangedependent, is customarily ignored or lumped with the other uncertainties surrounding detectability.

12.5.5 Swerling Case 1 Chapter 7, Section 7.10 indicated why even fairly small ship targets have many scatterers, no one of which usually predominates, and large enough dimensions for the TPM to become busy, with numerous close-packed lobes and nulls in the TPM, as Figure 7.15(/). As the target moves in a seaway, the fluctuation is generally reckoned to have Rayleigh distribution, although some authors suggest it may be better described by log-normal distribution (Chapter 11, Section 11.7.3). Fluctuation rate is linked to roll and pitch periods and is slow relative to the pulse repetition interval. Swerling Case 1 approximates this very important class of target. The model assumes RCS occasionally extends towards infinity, at which point probability is infinitely low. Practical targets come close to this extreme on the rare occasions a large flat hull plate comes exactly normal to the sight-line and reflects a highamplitude 'flash' (sometimes 3OdB above mean RCS). Writing mean RCS = O].

(12.14a)

(T/

As depicted in Figure 12.20, which is normalised by putting a — 1, this PDF falls smoothly, from 1 towards 0 when a rises from 0 towards oc. When a = a, p(cr) = 0.37, so on 37 per cent of occasions RCS exceeds average. More to the point, the remaining 63 per cent have RCS below average. A threshold set to detect average RCS will give Pp = 0.37, too low for the operator to be reasonably sure of perceiving the raw target on the display, or for effective track formation, manually or by ARPA/ATA. As usual, cumulative probability that the signal is less than the threshold, k, is found by integration: CP= f exp(--)dcr.

(12.14b)

Figure 12.20 shows this to be a curve from the origin which is more or less a mirror image of the PDF. Putting SNR = q (numerical), the PDF of signal plus noise is approximately as follows (the expression is exact for square-law detection).

,(^êxpf-IJL]

(12.15)

and

Substituting k = 2.146V— F per Eq. (12.6c) gives an expression linking PD with SNR and/Â:

P0 = exp \^1L]

=

X0FW+*)

(12 0.64 and is about 5 dB when Po t = 0.9. Diversity with AND logic output: here there is a system false alarm only when simultaneous false alarms occur in both channels: Âl

= V ^FAt-

Therefore F1 = \FX.

(12.27h)

If, for example, system false alarm probability is to be 10~~6 or 10~8, channel false alarm probability is set quite low at 10~3 or 10~4, with low detection threshold and hence low q\. The probability of the pair detecting a target is the square of one alone doing so, therefore PDI = /P^t-

(12.271)

Therefore

and P 0 1 = 10^/(2*1)1.

(12.27k)

Diversity improvement, dB

OR logic, F= - 8

OR logic, Fx= - 4 Light line AND logic, F = - 4 Light line AND logic, F = - 8

In noise Twin transmitters, single receiver In clutter

Overall PDV 'log' scale

Figure 12.36

Diversity improvement. Detection improvement relative to single channel. Swerling Case 1 target. Confirms the superiority of OR logic when high Po is required

Figures 12.35(c) and (d) illustrate the AND logic configuration. Although superior to a single radar alone, it is inferior to OR logic when P^ exceeds 0.6.

12.8.7 Combination performance Figure 12.36 plots diversity gain to a base of system Pot for the above combinations, for the same two values of system /VA exponent F t , confirming the superiority of OR logic. Diversity is most beneficial when high Po is required.

12.8.8 Practical problems All radars contain sources of error which degrade the reported positions of targets. Each radar of a diversity pair will have its individual position error, so if both outputs are displayed on a PPI, in general two paints will be shown. Is there one target, seen (at slightly differing apparent positions) by both radars, or is the first radar viewing one target, perhaps a tug, while the second radar has a nearby second target, maybe a towed barge, the tug being in a TPM null? The problem of error in plot association is discussed in Chapter 13. Combination of the outputs on a single display introduces circuit design problems, reduces operational flexibility (it would be difficult to optimise one radar for short range with the other set to a long range scale), and might compromise system integrity should one radar fail. Currently the pair of radars carried by ships operate almost independently, foregoing the potential benefits of diversity. Certain VTS stations do

operate twin radars in diversity mode, usually both at 9 GHz, sharing a single scanner by interleaving transmission pulses.

12.9

Detection of active targets

12.9.1 RTEs and superhet raeons The discussion of active devices in Chapter 8 did not examine probability of detection. Unsaturated radar target enhancers act as passive point targets whose fluctuation characteristics are governed by the antenna radiation patterns, which are usually smooth enough for the RTE to become a Swerling Case 0 non-fluctuating target, even when not ground-fast. The RTE receiver noise component of output adds a generally insignificant component to system noise. Receivers within saturated RTEs can be regarded as detecting all interrogations; PDI = 1, subscript 1 denoting interrogate leg. Racon receivers contribute noise but pick up no clutter, and see radar transmitters as non-fluctuating Swerling Case 0 sources. Because quite low sensitivity suffices to detect the one-way interrogation, receiver noise of superhet racons is small, their SNR usually being very high even when the interrogation is only marginally above receiver threshold, causing a rather sharp increase in PDI from 0 to almost 1. Because of the numerous interrogating radars within range, pulse to pulse integration is not normally possible, or indeed necessary. These racons have Ricean probability distribution as for non-coherent radar receivers, Section 12.3. Unless the manufacturer's data sheet indicates otherwise, one may assume the racon receiver threshold is set for no more than one false interrogation per 20 s, with PFA ~ 10~8 (Eq. (12.1), F = —8, bandwidth —5 MHz). The low false alarm rate provides a margin against deterioration in service, degradation at temperature extremes, and minimises both interference generation and battery drain. If a sidelobe suppression system adapts the threshold sensitivity according to interrogation strength or pulselength, PFA is sometimes yet lower. On the response path, the radar receiver picks up the usual noise and clutter. Active devices are point targets of rather smooth target pattern map and, when not combined with a platform of significant RCS, form Case 0 targets similar to passive point targets. Single-pulse SNR, q, is linked to PD by Eqs (12.8) and (12.1 Ia) and depicted by Figures 12.12-12.14. The benefits of integration remain available on the response leg. Observed at the radar display, overall PD is the product of the interrogation and response leg probabilities of detection, PDI and PD2, respectively (unless the response transmitter becomes overloaded by an excessive number of interrogations), each having to exceed the required overall value. When the racon is muted, PDI = 0. P0 = P01x

P02,

(12.28)

The extended nature of racon response paints assists visual perception on the PPI at lower PD than applicable to point targets. Indeed, the response tail may be displayed even when receiver swept gain has suppressed the initial portion; reliance should not however be placed on this effect, particularly as it causes range error. Considering

say a 10 |xs response as comprising 10 consecutive events when receiver bandwidth is say 1 MHz, the effective number of events integrated in the scan is multiplied by 10, improving SNR by at least 6 dB (non-coherent receiver, Figure 12.29) or 10 dB (coherent radar, Eq. (12.19b)). With this proviso, racons form Swerling Case 0 targets. Offset frequency racons are received by the radar through a special receiver channel. The channel-splitting arrangement is likely to worsen the noise figure by a few decibels, but little or no clutter will be received if frequency offset is sufficient, enabling the racon channel threshold to be reduced. As the scanner may be operated away from its design frequency, its effective gain may be somewhat reduced and its sidelobes raised; appropriate values should be entered in the radar range equation. Saturated RTE responses perform as Case 0 targets.

12.9.2 Racons, etc., with crystal-video receivers A crystal-video receiver with square law demodulator can be used when it is unnecessary to gather interrogation frequency data, e.g. in swept frequency racons; Figure 12.37 shows the essentials. Radar proximity detector devices and the enabling receivers of more advanced RTEs have similar sensitivity to racon receivers and may also contain square-law crystal-video systems. A 'crystal diode' demodulator when passing current generates several types of noise. • • • • •

Ordinary thermal noise in the spreading resistance. Shot noise in the p-n junction ('barrier noise'), caused by random electron emission, frequency distribution as for thermal noise. Thermal noise (noise figure ~2 dB) in the first stage of the following video amplifier. Flicker noise at low frequencies (below ~100 kHz). Noise density oc 1 / / . However, antenna and feeder losses and associated noise are negligible.

Crystal-video receivers have notoriously poor noise factors, caused by shot noise coupled with poor rectification efficiency. Luckily, the longest interrogation pulse of 1 MHz can be handled efficiently by a video amplifier whose bandpass filter's lower Antenna

Square-law video demodulator ('crystal diode') Square-law characteristic changes distribution

Circulator Protection

Threshold Makes detection decision

Filter

Noise. Gaussian distribution

Coder

Transmitter oscillator

Threshold voltage, K Baseband video amplifier Frequency control

Response

Figure 12.37

Crystal-video receiver. Shown as used in swept-frequency racon. Based on Figure 8.7, emphasising receiver components to detector

cut-off frequency is 500 kHz, keeping out flicker noise. The minimum pulselength of say 0.2 |xs needing full sensitivity determines the upper cut-off frequency (base band operation, Bn = 0.5/r, see Chapter 3, Section 3.5.7), so upper cut-off frequency is ~2.5 MHz and noise bandwidth is ~2 MHz. Sufficient receiver performance is just achievable by direct microwave demodulation without resort to low noise microwave pre-amplifiers. (Crystal-video receivers are capable of—72 dBW sensitivity at 9 GHz for F — —8 and 3 dB pulselength 0.2 jxs). Higher bandwidth may be preferred for proximity detectors, reducing sensitivity by a few decibels. Swept frequency racons directly detect the demodulated microwave signal without an IF system. The original Gaussian distribution is retained, except that the detector has essentially a square law characteristic (voltage out oc power in), so Section 12.2 applies but with halved dB values. The small noise contribution from the succeeding video amplifier remains Gaussian but is insignificant. Probability of detection of an interrogation, PDI, is calculated on a single-pulse Swerling Case 0 basis as follows. As with superheterodyne racons, rated sensitivity, say —70 dBW, is usually taken at a fairly high PDI , say 0.9. For a linear system, from Eq. (12.4)

«>.-;EH-J where #MHZ is bandwidth in megahertz, equating to ~15 m maximum for 1 MHz bandwidth. Likewise, when SNR is good, plots may tend to be rotated anticlockwise by up to half a beamwidth towards the leading edge of the scanner beam.

13.3 Errors in terms within radar performance calculations 13.3.1 Introduction This section summarises some sources of error within the calculations developed in earlier chapters. Because losses are generally imperfectly known, they introduce error to calculation of SNR, which in turn affects accuracy of calculated probability of detection.

Atmospheric attenuation, discussed in Chapter 5, Section 5.9, is entered as a specific loss term LA in the radar range equation. Many of the effects summarised below depend on wavelength, varying slightly within a single frequency band. Except when highest precision is required, it is usually acceptable to insert mid-band frequency or wavelength if actual values are unknown. It is never permissible to assume performance within one band describes performance in another; always re-calculate. Most or all of the following loss components are systematic. They may improve as the radar warms up in the first few minutes of operation - or deteriorate if it overheats - and may depend somewhat on range scale. Values ascribed to some losses may be arbitrary in absence of firm data. Relevant assumptions should always accompany SNR calculations.

13.3.2 Transmitter hardware losses This group, L t , includes all losses which reduce the radiated power below its nominal value. 1. Short-pulse loss of transmitter power. Modulator imperfections may reduce peak power by a couple of decibels on short pulselength. 2. Duplexer. Relative to the magnetron power output as reference, loss in the duplexer reduces power at the transceiver unit output by a few tenths of a decibel. 3. Feeder resistive loss. This depends on the length and type of feeder if there is one, see Chapter 2, Section 2.6.2, Table 2.2. 4. Feeder mismatch loss. This depends on the load mismatch (scanner, and rotating joint if a separate component), see Chapter 2, Section 2.6.2, Eq. (2.5b) and Figure 2.16. This loss remains if a transceiver is connected direct to a mismatched scanner with no intervening feeder and is 0.5 dB when VSWR = 2. Feeders are an unseen item, out in the weather and vulnerable to mechanical damage leading to additional mismatch and water ingress or condensation, raising loss. 5. The scanner. This contains several loss components, generally included within suppliers' quoted overall gain figures (Chapter 2, Section 2.7.16), so rarely needs further consideration. When VTS and range surveillance system parts are individually sourced from specialist suppliers, one must properly account for losses in rotating joints, etc. Scanner losses total about 2.5 dB excluding beamshape loss.

13.3.3 Service loss Achieved in-service performance of new equipment depends on the amount of tender loving care bestowed by the installation team. Among other things, swept gain law and scanner tilt need matching to scanner height, range zero has to allow for feeder transit time and some data extraction settings depend on scanner azimuth aperture. Scanner bearing has to be collimated to the ship centreline. VTS and range surveillance sets have to be surveyed-in relative to chart datum, and it may be necessary to correct for latency in data transmission to the central processing system. It is fair to assume that properly installed and maintained modern equipment in good working order meets the minimum values of transmitter power, noise figure, etc.,

promised in the manufacturer's data sheet with allowance for any installation-specific factors such as feeder loss. New equipment may exceed the minimum by a couple of dB, but this cannot be relied on. Any margin in hand gives a cushion against some of the uncertainties always surrounding environmental effects and target RCS. Provided there are no untruths, the supplier may legitimately highlight strengths without dwelling on weaknesses, so data sheets should be read forensically without jumping to unwarranted conclusions. For example, radar transmitter power may be stated at the magnetron flange rather than at the feeder input. If so, one should enquire the intermediate losses in the duplexer, or at least make an informed guess based on Chapter 2, Section 2.3.2. It is prudent to assume system performance gradually deteriorates to an extent dependent on the roughness of operating service, quality of manufacture, use made of built-in test equipment and the servicing policy. For example, magnetrons slowly lose power and moisture may leak into feeders. Radomes and scanner windows are finished with self-cleaning slippery surfaces to help shed dirt, water and ice. Minor surface grime has little effect but thick buildup of ice or dirt, especially soot, may introduce attenuation and mismatch losses. Many ordinary paints are lossy and have rather high dielectric constant so should never be applied to radomes and windows, but sometimes are. Digital technology makes modern radars far less prone than their analog ancestors to in-service deterioration as components drift, and offer few preset controls as hostage to those dubiously qualified servicing technicians who come aboard in foreign ports. Nevertheless, it is prudent to include a service loss term in the radar range equation to allow for minor shortfalls in performance parameters. The receiver service loss (Chapter 3, Section 3.2.2), say 1 dB, comprises scanner deterioration through dirt, etc.; feeder deterioration; loss of noise performance as the TR cell and mixer crystals age, and minor local oscillator tuning errors. In absence of specific data, transceivers sheltered from the weather and not subject to temperature extremes may suffer 1 dB transmitter service loss. Where the transceiver is located at the mast-head, it is prudent to allow a couple of decibels additional service loss each way at temperature extremes. Service loss assumptions should always be stated with calculations.

13.3.4 Receiver hardware losses The scanner losses recur on the receive leg, as does the feeder resistive loss. Mismatch loss is normally that of the transmit leg. Polarisation loss occurs if the target effective RCS is reduced by the chosen polarisation, for example, corner reflectors with circular. The duplexer and protection circuit (Chapter 3, Section 3.2.3) introduce loss, most conveniently expressed as raised noise temperatures, or incorporated within the system noise factor or noise figure. The effective noise bandwidth depends primarily on the receiver bandwidth, which we have taken into account, but also to a small degree on the (usually unpublished) shape of the response curve. The effect is small, best handled within the service loss.

Published parameters naturally assume the radar is set to full sensitivity and the possibility of the operator desensitising the receiver using the differentiator control or by turning down control settings should be considered. Receiver noise figure or factor is quoted in data sheets, either overall or for the first stage or LNA, in which case system noise figure is likely to be a decibel or so poorer. Noise figure deteriorates with age, especially if there are gas TR cells. Full use should be made of any performance check facilities; it is worthwhile to confirm which parts of the radar these embrace.

13.3.5 System processing losses The following losses total about 8 dB in non-coherent modern marine radars. •

•

•

•

•

Beamshape loss. The assumption, made for ease of calculation, that the scanner beamshape is rectangular causes a beamshape loss (Chapter 3, Section 3.3.1) of about 1.6 dB (two-way) to non-coherent systems, about 2 dB to coherent systems and maybe as much as 4 dB when the platform yaws, rolls or pitches through a beamwidth. Scanning loss. The angular movement of the scanner between transmission of an interrogation and receipt of the echo was discussed in Chapter 2, Section 2.7.15 and is usually negligible. Filter weighting loss. For ease of calculation, we assume the receiver filter has rectangular frequency response, and the filter to be matched to the transmitted spectrum, together causing 1-3 dB loss, see Chapter 3, Section 3.5.2. Quantising loss. In general, the analogue voltage when digitised leaves a remainder which is ignored, causing a random error of 0.0834 x least significant bit power (—10.79 dB). Meikle [1, Section 10.4.1.1] quotes quantising losses for differing number of significant bits representing the noise as 0.35 dB (1 bit), 0.09 dB (2), 0.04 dB (3), 0.03 dB (4) and 0.01 dB (6 bits). Quantising error. This error arises when an analogue signal is digitised, because 1 bit may not quite equate to 2:1 voltage ratio. Where x is the least significant error expressed in error standard deviations, Meikle f 1, equation 13.21] gives: Quantising error = J

• • •

•

/ 1 H-jc 2

.

(13.7)

Straddling loss of say 0.5 dB arises from the echo on average not sitting squarely within a single detection cell, see Chapter 3, Section 3.6.3. Overflow of large targets beyond a single detection cell in azimuth and/or range reduces cell RCS, see Chapter 10, Sections 10.7.1 and 10.7.2, respectively. Integration loss arises when the returns are imperfectly integrated, Chapter 12, Section 12.6.3. This loss is dependent on the radar integration scheme, the number of pulses and the fluctuation characteristics of the target, and includes: Operator loss if a cursive display is employed as the integrator (L op , Chapter 3, Section 3.10.3, Eq. (3.5)).

13.3.6 Point target responses The fairly uniform azimuth polar diagrams of most point reflectors can be severely degraded by interference effects with the host structure skin echo, Chapter 7, Section 7.10. Mean RCS is often only mildly frequency-dependent, but all active devices and a few passive reflectors such as the resonant patch type may have sharp band-edge cutoff. Here special attention should be paid to systems including radars working at or beyond the edges of the recognised marine bands. Echo strength depends critically on multipath interference (see Chapter 5, especially Section 5.3, Figure 5.4), which in turn depends on height and atmospheric refraction, which itself changes with weather or time of day. As shown in Chapters 7, 8 and 12, RCS of point reflectors tends to be somewhat less uniform than that of active reflectors, but the fluctuation of the reflector alone probably remains approximately Swerling Case 0, the combination with the structure skin echo approximating Cases 3a or even 1. RCS of most passive point targets depends on the fourth power of frequency. The radar bands are about 2 per cent wide, so calculations assuming centre-band are likely to be in error by about ±4 per cent (0.18 dB) at band edges. As noted in Chapter 8, Section 8.4.3, poor interrogation strength at frequency agile racons causes response frequency jitter. Frequency error Sf depends on interrogationleg SNR, q, per Eq. (8.3b); 8f = — - = Hz rms.

xjlq If, say, radar receiver bandwidth is matched at B = 1/r and Sf = B/4 (giving ~1 dB loss), q = 8 numerically, or 9 dB. The distinctive responses of racons and SARTs are visually decoupled from any echoes of the host structure and are therefore non-fluctuating, Swerling Case 0. Although an RTE on its own may have an excellent radiation pattern and Case 0 response, in practice it usually operates with a host vessel having significant skin echo. As shown in Chapter 8, Section 8.15, the composite pattern is not uniform and may have Swerling Case 3a or Case 1 fluctuation characteristic, raising the necessary SNR for high P0. Saturation range of RTEs depends partly on the RTE itself, but partly on the radar and environmental parameters, so if these are changed system performance should always be re-calculated, rather than merely inserting the unsaturated RCS in the radar range equation. Heavy traffic may overload active devices, restricting the number of responses received by an interrogator and precluding achievement of high PDAlthough antenna gains, receiver sensitivity and transmitter power of active devices may vary across the band, individual frequency dependencies are rarely quoted in data sheets, to reduce test cost and because there may well be deviceto-device variations. Assuming the data sheet gives minimum values throughout the band, performance may turn out a couple of decibels better at a spot frequency. Performance may drop abruptly at band edges and it is never permissible to assume active devices work at all outside their declared bands.

The circuits of many active devices are poorly shielded from ambient temperature, perhaps raised by sunlight, and have to be designed to operate between say +55 0 C and —200C for tropical and temperate locations, and lower for high latitudes or Eurasian or North American continental winters, where —200C is not thought cold. Failing specific information, it is prudent to assume a couple of dB shortfall of receiver sensitivity and response power at temperature extremes.

13.3.7 Extended target RCS Ships' RCS are rarely certainly known and are likely to vary significantly with aspect, radar band, deck cargo and other factors. Values may sometimes be deduced from observed detection range, otherwise RCS will have to be inferred from empirical data such as those in Chapter 10, Section 10.4. RCS usually rises somewhat with frequency. Depending on aspect, effective RCS may fall when the target dimensions overflow the detection cell at short range. Coast echo strengths are even less certain, and may vary with wet or dry weather or seasonally with vegetation growth.

13.3.8 Scanner rotation The small rotation angle traversed between sweeps, SO, depends on prf and rotation rate, introducing an angular error which Meikle [1, p. 395] quotes as: SO error ~ —= = 0.28950 rad rms.

(13.8)

Vn Typically, for lOOOpps and 2.5 s scan time, error = 0.042° rms and is negligible compared with the beamwidth. Centroiding is a computational method of reducing error of a number of azimuth measurements of varying amplitude, giving more weight to readings taken when SNR is high and error low. Range may be similarly centroided. Centroid target bearing (or range) = sum of the individual azimuth (or range) measurements x their signal strength products divided by the sum of the signal strengths.

(13.9)

13.3.9 Environmental conditions Atmospheric refraction plays little part at short range but may dominate long range detection, see Chapter 5, Sections 5.2 and 5.3. Not only do refraction index, n, and its height variation depend on weather and time of day, causing considerable variation of refraction factor, k, but ducting may be sufficiently severe to change maximum detectable range by a factor of two or more. These very important effects are generally not predictable, easily measured or readily inferred from meteorological instrument readings. It is best to calculate performance for a range of refraction values, including

low values of &, which, although perhaps infrequent, may be allied to bad weather in which radar performance is vital. Hydrometeors introduce attenuation and noise into the radar-target path. Attenuation depends on the path length and is negligible at short range or when the precipitation is localised. Performance calculations should therefore state the path length over which precipitation is assumed present, whole path being the worst case. Precipitation also introduces clutter, which may be severe, see Chapter 11, Sections 11.4 and 11.5. Although it is rarely feasible to assess distant precipitation rates, at least the operator can adjust the radar to display and assess the severity of precipitation clutter, and in daylight it is often possible to see distant squalls. Clutter is chiefly significant when it surrounds targets. Clutter elsewhere may be significant if it causes the data extraction system or the operator to adopt suppression tactics which reduce in-clear target detectability, for example provoking short pulse operation which improves signal to clutter ratio for any targets lying within a squall at the expense of the signal to thermal noise ratio elsewhere. It may be necessary to recalculate for each available pulselength to determine optimum performance. Attenuation and clutter rise non-linearly with precipitation rate, and also depend on precipitation type and on atmospheric temperature, neither of which may accurately be known. Fog can cause moderate attenuation but negligible clutter. It is not normally possible to detect fog banks by marine or VTS radar, making it difficult for the observer to forearm against performance loss. The sea surface roughness at the grazing point affects strength of the forwardreflected indirect ray, and hence the resultant ray. This introduces moderate uncertainty of echo strength for extended targets, and very considerable uncertainty for point targets, active or passive. Surface roughness at the target also retro-reflects as sea clutter (Chapter 11, Sections 11.6 and 11.7) and is often the limiting factor in target detection. As with precipitation, clutter elsewhere may bias the operator into choice of short pulse, spoiling detection of any targets surrounded by more benign local clutter. Alternative definitions of wave height are enumerated in Chapter 5, Section 5.7.4. Care is necessary to specify which is in use, a problem avoided when using sea state number. Sea roughness is somewhat difficult to assess, and may vary within the display area, particularly when a harbour VTS looks out toward the open sea. The effect of a given wave height also increases from a swell to a fully developed sea, driven by a local wind; whether the wind is rising, whether the radar is looking up-, down- or cross-wind and by plane of polarisation. The distribution of the clutter amplitude also becomes wider in heavy seas, see Chapter 11, Section 11.7.4. Tide may vary effective scanner and target heights, depending whether the radar and its target are afloat or ground-fast. It should be remembered that the indirect ray grazing point may either be the water surface or terrain of some kind, possibly tidal mud-flats. Point target multipath null ranges can vary significantly with tide and it may be worth calculating for several tide states, or at least for low and high

water ordinary spring tides. Coastal echoes can also vary considerably if, say, a beach covers at high tide.

13.4 Accuracy of calculations leading to SNR or PD 13.4.1 Approximations within calculations Previous chapters quantified environmental factors such as precipitation attenuation using algorithms, whose form may or may not be closely linked to the underlying physical process. Usually the algorithm matches some experimenter's observed results. The experimental conditions may not be quite identical to the current scenario, introducing error. Published equations do not always lend themselves to calculation. Sometimes we have offered approximations, accompanied by indications of their error. For example, in Chapter 5, Section 5.8.4, the reflection coefficient of surface roughness, po> as given by the experimenters Brown and Miller, is represented by the algorithm of Eq. (5.41 c). Its inconvenient Bessel function Eq. (5.4Id) can be approximated by Eq. (5.4Ie), the error within the approximation being graphed in Figure 5.21. The considerable uncertainty typical of radar data makes precise calculation impossible so it is misleading to express results to many significant figures. On the other hand, premature rounding of the individual terms in an equation introduces unnecessary error in the final result. It is best to insert each term to one more decimal place than its precision warrants, then round off the final result to one place less than the least certain important term. For example, we might judge that our antenna beamwidth of nominal 1.0° actually lies somewhere between 0.95° and 1.05° (0.01658-0.01833 rad). When calculating formulae, we would insert 0.0175 rad (1.0°) but round off the result to two significant figures. Computer spreadsheet methods of calculation facilitate analysis of the likely accuracy of results by repeat of calculations at upper and lower limit conditions. Rounding is deferred until the end of the calculation chain. The standard statistical methods for uncorrelated variables can also be used. Beware the seductive influence of the computer printout containing umpteen significant figures. If the input is rough, the output cannot be better. Most of the digits will be dross. Often it is enough to round off results to the nearest decibel (26 per cent) and even that may overstate the real precision. This cavalier attitude may initially shock readers used to the exactitude of accountancy. Be assured that engineering budgets are never drafted on the same principle (well, hardly ever). Throughout, we have stressed that system performance is hedged about with uncertainty, and we have just mentioned enough error sources for the pessimist to assert that all results of performance calculations must be meaningless. This is not in fact the case; most of the error sources are of moderate size and are uncorrelated, so the standard deviation of the resultant error is much less than the sum of the moduli of the individual component errors. Furthermore, depending on the task in hand, many of the error sources are inoperative or more or less cancel out, as described in the following task scenarios.

13.4.2 Radar comparisons It is often necessary to answer practical questions such as: In a defined environmental scenario, is 9 GHz Radar A, with certain datasheet parameters, better than 3 GHz Radar B, having somewhat different parameters? Here it is fair to take each radar's transmitter power, scanner gain, etc., at face value, or at least apply the same service loss to each. An arbitrary representative target type can be used, such as a small uniformly extended target of exactly 20 dB m2 RCS (perhaps dropping 5 dB at 3 GHz per Chapter 10, Section 10.4.6, Eq. 10.5) and exactly 10 m effective height. Scanner height can be set at some exact value, such as the nominal height above sea level of the host ship's radar platform. Atmospheric refraction can be set in turn to several nominal values, say k = 0.80, 1.333 and 2.0. Precipitation rate can be set to a representative value, say heavy stratigraphic rain of 16mm/h whole path at 200C, so defining nominal atmospheric attenuation and precipitation clutter. Similarly, sea conditions would be set at a representative nominal value, so defining indirect ray reflection, multipath coefficient and sea clutter. It is immaterial that these nominal values may never simultaneously occur in practice. Small errors within the algorithms representing attenuation, clutter, etc., also almost cancel, leaving only negligible residual errors in the comparison. Using a spreadsheet, to be described in the next chapter, we could plot SNR or even PD to a base of range. The intercept on the individual radar's minimum detectable signal (or minimum acceptable fb) then indicates maximum usable range. Both radars should be calculated with optimised control settings, e.g., pulse length. For example, Radar A might show 21.3 km and radar B 23.0 km, indicating the latter is more sensitive under the chosen conditions, giving 1.7 km more range. Put into actual service and measured with precipitation and sea states judged similar to the above paper figures, the above ranges are unlikely to be exactly observed, but it is very likely that Radar B would continue to exhibit about 1.5-2 km advantage. Similarly, if the scanner heights were actually 12 m rather than 10 m, the advantage would not change much. To confirm Radar B's superiority, the calculations should preferably be repeated for a family of clutter scenarios and target sizes.

13.4.3 Mounting heights Low scanner height minimises sea clutter, but great height gives longer horizon range and probably longer detection range except in heavy seas. Shipboard, height is likely to be constrained by the need for all-round visibility, but sometimes some limited choice is available. VTS and range surveillance systems are often bought against contractual requirements to detect or track specified small targets throughout a specified sea area in specified clutter, payment being subject to on-site acceptance trials. This can present bidders with severe problems. Should one go for a relatively high number of out-stations, mounted low, each having rather poor horizon range, or go for fewer stations with higher masts and narrower-beam scanners to bring the clutter back down? Out-stations incur high first and maintenance costs - access roads, security fences, buildings, power supplies, data links all have to be considered

and land may be difficult to acquire. On the other hand, large scanners with stiff tall masts having safe maintenance access aloft are also expensive and may raise aesthetic objections. We shall return to this question in Chapter 15.

13.5

Plot and track accuracy

13.5.1 Instrument errors Range is determined by the radar as the time delay between transmission and reception, and then measured by the operator using the display's electronic range marker or rings. Both these in essence rely on a quartz crystal oscillator and digital counter arrangement. The oscillator is inherently accurate and stable to better than 1 part in 106, so instrument range errors are small, systematic and largely self-cancelling when determining velocity or target-to-target separation. Bearing on raster displays depends on digital retrieval of the initial R, 0 information from the scanner, tagged with scanner azimuth, usually 1024-4096 positions per scan and measured against an electronic bearing marker, digitally generated and driven from the gyro or compass. Again, errors are small and mainly systematic. When displayed raw, the paint angular width approximates the target ship's projected width plus the scanner beamwidth. When the raw target is displayed: echo width = ship width + scanner subtended beamwidth.

(13.10a)

In length, to minimise the risk of parts of the target lying closer than indicated, and to eliminate echo stretching when a target ship presents an open hold which acts as an echo box, sometimes only the leading edge of the echo pulse is used, discarding the pulselength-dependent body of the pulse. Ship length then becomes immaterial. Here: echo length = pulselength x c.

(13.10b)

Track formation is basically the generation of a straight line representing target velocity through a succession of plots laid down at successive instants, by use of computational algorithms. It is convenient to represent each target position as a point, drawing the best straight line among the points by regression (defined by Clapham [2] as a statistical procedure to determine the relationship between a dependent variable and one or more explanatory variables). Tracking aids tend therefore to show plots as synthetic points representing either the leading edge as just remarked, or the echo 'centre of gravity', rather than painting the whole raw echo area. In the latter case particularly, the resulting crisp display masks glint and fails to warn that some part of the target may lie closer to own ship.

13.5.2 Ship motions Beside progressing smoothly along the course made good, ships also pitch, roll, yaw, surge, heave and sway to degrees dependent on sea state. The first three are oscillatory

angular motions about the transverse, longitudinal and vertical axes respectively, the remainder being oscillatory bodily displacements about those axes. Ships may also carry trim or list/heel, semi-permanent components of pitch or roll, respectively. These eight displacements in effect move the ship's scanner about, introducing error when projected from the scanner to waterline level, the positioning plane of primary interest to the navigator. Pitch, roll, surge and sway displace the scanner from its normal position, which is vertically above the nominal position relative to the average course made good. Pitch and surge cause the scanner to oscillate about the ship's mean forward velocity, while roll and sway introduce an oscillatory transverse component. Relative to own ship's waterline position, or the bridge, all targets appear to take on complementary oscillations. Motion periods (~10s) are more or less constant for a given ship, but as they are decorrelated from scan rate, target positions are subjected to near-random errors on successive scans. Severe roll or pitch swings targets lying near to the roll or pitch plane through the scanner elevation polar diagram, the effect becoming severe when peak roll exceeds half the scanner elevation beamwidth (IMO require sufficient beamwidth to cater for ±10° roll). Chapter 12, Section 12.10.2, discusses resulting P0 fluctuation. The relationship connecting roll amplitude to sea state for a given ship is rarely published and varies with relative bearing of wave fronts, ship speed, condition of loading (in particular as it affects metacentric height), wave period and perhaps other factors. Insertion of inappropriate values is likely to introduce error into calculation of PD in heavy seas. Roll or pitch can also introduce cross-polarisation, as discussed in Chapter 8, Sections 8.12 and 8.13, rarely with significant effect on echo strength. Yaw, unless detected and allowed for, causes targets to oscillate in apparent bearing, introducing bearing error. The echo may spread among several detection cells, reducing hits per scan and spoiling Pp. Yaw may also blur actual changes of target bearing, making target manoeuvres difficult to spot. Heave varies effective scanner height, which is usually only significant when it oscillates point target null ranges. Of course, targets afloat may also heave, modulating target height. Target roll and pitch introduce second-order and usually negligible height reductions.

13.5.3 Scan plane tilt errors For analysis of tilt error, we assume a flat Earth (curvature merely introduces secondary errors at extreme range) and disregard all other instrument errors. The geometry is shown in Figure 13.4. With the radar platform on an even keel, the scanner axis is vertical with the scan plane horizontal. Surface targets at true azimuth 0 rad from tilt axis (for example the fore and aft line if the platform rolls) are displayed at azimuth 0, here coinciding with 0 . A target at range R has true polar coordinates R, 0 , which may be resolved into Cartesian coordinates R cos 0 and R sin 0 along and normal to the tilt axis, respectively. When the scanner plane is tilted at angle v to the horizontal, the along-axis intercept on the scanner plane is unchanged, but the

Error

heel

Shaded: areas of weak echo where target lies outside elevation half-power point

Target bearing relative to tilt axis

Apparent bearing, 9 True bearing, 0 Horizontal plane Radar

Scanner plane Apparent target Target true position Tilt angle, v

Tilt axis

Figure 13.4

Geometry

Scan plane tilt error. Severe pitch or roll introduces angular positioning error which depends on target bearing

normal intercept increases to R cosec v sin 0 . Apparent azimuth bearing, 0, always lies further from the tilt plane and is given by tan# = cosec v tan 0 .

(13.11a)

Figure 13.4 also plots the angular error, 0 — 0 . Small when v < 5°, error rises in a square-law fashion with inclination, exceeding 4° when the platform rolls or pitches severely to 30° peak value and the target bears ±45 or ±135° to the tilt axis, for example, when the target is broad on the bow or stern quarters. In general, platforms roll or pitch asynchronously with scan rate, so quartering-target apparent bearings are subject to a quasi-random error which may be significant, sometimes exceeding the scanner beamwidth. In the hatched areas of the figure, the scanner boresight also inclines sufficiently to take the target outside the half-power elevation beamwidth, weakening the echo by more than 6 dB. Figure 13.5 plots the bearing error fluctuation for a quartering target, seen from a sinusoidally rolling platform. The error is unidirectional, giving an angular mean bias proportional to the square of the peak tilt. In practice, mean errors may be reduced by the echo weakness or complete loss at tilt extremes. The target fluctuation characteristic, if not already Swerling Case 1, also migrates towards Case 1, because whole scan packets become correlated, see Chapter 12, Section 12.10.2 and Figure 12.39. The low SNR may reduce positioning accuracy, as shown in Section 13.5.4.

For worst case, target at 45° to tilt axis.

Instantaneous error

Peak roll 30° (m ;an error 2.01°)

Time, relative to complete roll cycle

Figure 13.5

(Time frame -10 s)

Bearing error fluctuation through platform roll cycle. Both systematic mean error and quasi-random errors are introduced by rolling or pitching

When the target is normal to the roll axis ( 0 = 90°), the range measurement is subject to H tan v range error. At other bearings, range error= / / s i n G t a n v m .

(13.11b)

For example, if H = 35 m, 0 = 90° and v = ±15°, range error = ±9.4 m. This error is equally disposed about zero with no position bias. When roll is extreme, the target will again fall off the nose of the scanner elevation beam, reducing strength of some of the echoes. A saving grace is that high scanners tend to be associated with large ships having less roll and pitch. Expressed as linear displacement from true position, angular error is more important than range error except at subkilometre ranges. In principle, tilt-related errors may subsequently be corrected by algebraic processing, tilt being sensed by an orthogonal pair of clinometers. A floating electronic bearing line is often provided to enable the operator to measure range and bearing between a pair of targets. Here systematic errors cancel but random errors accrue independently for each target and the readout error will approximate \fl the random error component of a single target relative to own ship, whose position within the system is of course accurately known.

13.5.4 Effects of SNR and bandwidth on plot accuracy The following error expressions are approximations taking no account of detection cell size, straddling between adjacent range bins or some other secondary factors. Just as we tend to make more accurate length measurements by ruler when the light is good, the accuracy to which radar determines the position of a point target depends in part on numerical SNR, q. It is a fact of statistics that any measurement made with

basic resolution x has error 8x where: Sx ~ -^= m rms.

(13.12a)

sflq For range cell size R, receiver bandwidth B and velocity of propagation c, and if q is not very low, range error SR is 8R~—!^=m rms. (13.12b) 2BoJIq If say B = 1 MHz and q = 5 (7 dB), 5/? = 47 m. Increasing 4 by a factor of 20, to 100 (20 dB), or increasing bandwidth to 4.5 MHz reduces 8 R to 11 m. Except at the shortest ranges, 47 m position uncertainty might seem trivial. But radar is not employed solely to give nowcasts; plotting aids predict future target positions, based on historical course and speed. Speed is computed as rate of change of apparent position from scan to scan. If, say, range is measured with errors of +47 m one scan and —47 m the next scan 2 s later, radial speed component will have 47 m/s = 169 km/h error. Even with good SNR of 20 dB (q = 100), and inspection time of five scans, error may be 16 km/h, introducing 8 km error in a position prediction made for 30 min hence. Random bearing error 80 depends on the basic angular resolution AO, which approximates scanner azimuth beamwidth, 0. Doubling aperture at a given operating frequency halves 80 and tripling wavelength by shifting from the 9 to the 3 GHz band, while retaining the same aperture length, triples 80. 80 ~ -^=.

(13.13)

13.5.5 Plotting aid prediction accuracy Yaw, roll, etc., cause minor changes in aspect so echoes are received from successively different reflecting elements within a large target. This glint adds further error. As usual, range and bearing errors diminish as (a) more measurements are taken (b) through a longer inspection time. Unfortunately, the longer the inspection time, the less able is the predictor to cope with sharply manoeuvring targets and the longer it takes to realise that the target is manoeuvring. Accuracy of tracking aids such as ARPA or ATA (Figure 13.6) therefore demands higher SNR than necessary merely for reasonable PD of echoes on the display screen. It is the need to take many measurements over a substantial inspection time which can make new target tracks so irritatingly slow to form. Manual plotting is no better; to allow reasonable screen displacement between one plot and the next, about 3 min should elapse, and a third confirmatory plot should be taken after a further 3 min. Allowing for appraisal, manual establishment of a reliable track line takes some 7 min, during which range may have closed by up to 10 km. Figure 13.7 shows part of a display screen. Part (a) is a historic target plot at time TO, t s ago. The figure shows four alternative plot positions, aO, bO, cO, dO, each spaced around an error circle of radius e, \a from true position /?0, where 0 is the standard deviation. Because the error is random, the displayed plot could lie

Figure 13.6

Shipborne display with predicted vectors. Vector lengths ahead of the targets are proportional to the trail lengths behind them. Clutter speckles barely discernible. Data on the target marked 2 is presented on the alpha-numeric field to right of the display. Original in colour. Reproduced by permission of Kelvin Hughes Ltd, Ilford UK elsewhere, inside or outside the Ia circle. Part (b) shows the current set of possible plots a l , . . . , at time Tl9 circling true position pi at radius e. Line /?0, pi represents the true target movement in time t, and is the target's velocity vector. As noted earlier, the display must be able to show forward predictions of target movement, called vectors. Modern radars therefore can display predicted tracks for operator-selected forward times and deliver information of closest point of approach etc., as shown in Figure 13.6. To predict where the target is likely to be mt seconds into the future at time Tl, all that an operator or a machine computation can do is to extend velocity plot pO, pi by drawing a straight line through the two observed positions, extended for a distance proportional torn, so that length al, a2 = ra(aO, al). If there were no error in either displayed observation, the line would lie through pO and pi and extrapolate to p2, the true future position of the target. If however the observed positions happened to be aO and al, the predicted position would be at correct range but erroneous bearing, point a2. A similar result arises if the points were cO, cl, c2. If the points were bO, bl, b2 or dO, dl, d2 bearing would be correct with erroneous predicted range. Figure 13.7(d) shows a set of possible predicted track vectors al, a 2 , . . . , dl, d2, obtained by extrapolating the existing vectors aO, a 1 , . . . , dO, dl in bearing and speed. The predicted vectors lie on a circle radius V2me, so it is fairer to draw a smaller circle of radius me to represent the Ia locus, defining points a'2,... , d'2. In the figure, m = 2, but in service a short set of observations, perhaps spanning 30 s, are often used as the basis for quite long-term predictions, up to perhaps half an hour, with m as high as 60. If the Io error in such a prediction is to be 1 km (about the roughest prediction ever navigationally useful), the Ia error e of the two plots has to be as low as 1000/60\/2 = 12 m, necessitating good SNR, wide bandwidth, wide scanner aperture and little rolling or pitching, especially if using a small scanner or the 3 GHz band where angular resolution is necessarily less.

Figure 13.8

Prediction with systematic and random error. Systematic error component is not multiplied when predicting far ahead. Elliptical randomerror loci

For simplicity, the above examples assume equal along- and cross-track errors, giving circular loci. Beside SNR, the Xo plot error locus depends in range on pulselength, and in bearing on scanner azimuth beamwidth x range, so in general each plot Xo error locus is an ellipse with axes aligned on target bearing. Ellipticity varies with range, Figure 13.7 representing the special case of zero ellipticity. Systematic error (e.g. due to rolling) may bias the centres of all the ellipses from their true positions, as shown in Figure 13.8, which retains the previous notation. The locus of Xo error in the prediction is also an ellipse. The prediction extrapolation does not magnify the systematic error component. Of course, the radar makes not merely two but a dozen scans within a 30 s observation set, in effect integrating more echoes and considerably refining the prediction. Figure 13.9(MIR. Enter the operator-selected mode in cell F24. In the example, if F24 = 1, the spreadsheet would have assumed mode 1 parameters when computing for ranges < 1.5 nmi, mode 2 parameters for ranges between 1.5 and 3 nmi and modes 3 upwards for longer ranges; in other words, it is assumed that the operator sets range scale to the shortest which will display the target without offcentring. If the operator is using the 6 nmi scale, enter mode 3. The parameters of this mode will then apply at all ranges up to 6 nmi, with automatic changeover to mode 4 parameters when target range lies between 6 and 12 nmi and mode 5 parameters beyond. Charts of, say, SNR to a base of range may have steps at the mode boundary ranges as, say, receiver bandwidth changes; examples are included in Chapter 15. If F24 = 3 and no higher modes have been entered, mode 3 parameters are applied at all ranges. The mode facility allows short range performance to be computed with short pulse, etc., without wrongly allowing the user to assume conditions not available to the operator, such as short pulses and high prf at long range. If F24 is set to, say, 3, then medium-range parameters will remain in use at the shorter ranges, mimicking operator retention of a long range scale when viewing a close-in target. Enter the pulselength used on each range scale in column D26: D31; if the radar has SP/LP facility (cell F23), enter the long pulse settings in column E26: E31. Enter appropriate receiver bandwidths in cell F26: F31 and pulse repetition frequencies in column G26: G31; it is assumed that bandwidth and prf are not changed by the SP/LP switch; if the radar changes these parameters, enter the new parameters manually. Cells H26:H31 display the active mode. Cells 126:131 show the selected pulselength and J26: J31 show the number of pulses integrated for the scan rate, azimuth beamwidth, prf and is doubled for correlation over two scans if B20 = y.

14.2.8 Environment panel Enter environment type in cells H4 and G5 : H5, free text, say 'typical winter North Atlantic'. Enter atmospheric refraction coefficient, k (>0) in cell H6. The 'standard' value is 1.333 but lower values occur in bad weather, higher in good (Chapter 5, Sections 5.2 and 5.3). The effective Earth radius, E km, shows in cell H7 per Eq. (5.1). Cell BC29 uses the effective values of H9 h and E (cells AI29, AK29, H7, respectively) to compute horizon range, km, from Eq. (5.23a), independently of the main matrix. It is shown in the chosen units within cell J14. In cell H8 enter the precipitation or fog type: Stratiform rain = 1, Orographic rain = 2, Thunder rain = 3, Ice crystals = 4, Wet snow = 5, Dry snow = 6, Advection fog = 7, Radiation fog = 8. Cell G9 shows Fog visibility, km, if appropriate, otherwise Precipitation rate, mm/h. As prompted, enter in cell H9 either fog optical

visibility, V km, or precipitation rate, r mm of rain equivalent per hour. Cell HlO shows the equivalent stratiform rain rate for attenuation calculations, per Eq. (5.46d) if either of the fogs was selected, otherwise the precipitation rate set in cell H9. Cell Hl 1 shows the appropriate precipitation clutter RCS per m2 suiting the precipitation type in cell H8, obtained from Table S4, (cells BV22: CD28 reproducing Table 11.1 and Eq. (11.7)). In the table, an artificial 0.000001 is added to the HlO rain rate to avoid — oo problems when HlO = O. Fogs cause no clutter. Cell Hl2 shows the precipitation loss, /p dB/km one-way per Eq. (5.43), appropriate to the weather and frequency; if cell B6 < 5000 MHz, 3 GHz values are used; between 5000 and 12 400 MHz, 9 GHz values and above that J band values; intermediate frequencies such as 6000 MHz may therefore suffer some error. Precipitation and fog do not always extend over the whole radar - target path. Enter the extent (from 0 to 1 p.u.) of the path subject to the precipitation or fog in cell H13, guided by Eq. (5.44). Cell Hl3 defaults to 1 (whole path) even when Hl3 = 0. The spreadsheet assumes the target always to lie within the clutter. Enter air temperature (degree Celsius) and relative humidity (RH, from 0 to 100 per cent) in cells H14, Hl5, respectively; Cell Hl6 shows the clear air loss, Lc dB/km one-way per Eq. (5.49b). Enter significant wave height, /i s m, in cell Hl7. Equivalent sea state number appears as an integer 0-5 in cell Hl 8, obtained by lookup of cells CG24: CG29 within Table S5 (cells CF22: CM29), which is based on the modified values within Table 5.3. This is admittedly not entirely satisfactory, with steps from one sea state to the next (it would also be possible to connect sea state and wave height by Eqs (5.38) of Chapter 5, Section 5.7.5), but is the best available in absence of a reliable function smoothly linking hs to sea clutter. Enter in cell Hl9 the sea clutter wind factor (C2 = —2.5 to +2.5 dB for looking downwind to upwind, respectively, and several dB negative for a swell rather than a fully developed sea). The spreadsheet extracts working values for factors A, B and C of Eq. (11.11) from Table S5 cells CM23 :CM25, adding factor C2 to factor Cl (from Table 11.3 according to the scanner polarisation, cell F20). Weibull exponent, c, is computed from sea state in cell CM26 per Eq. (11.19) and Weibull weighting factor, W dB Eq. (12.13b), in cell CM27. Table S5 recognises only the 3 and 9 GHz bands, with changeover at 5000 MHz, and does not interpolate for other frequencies per Eq. (11.1 Ib). Enter, in cell H20, the average time proportion (from 0 to 1) that most of the target is screened from the scanner by sea waves, default 0. For the water or land surface at the grazing point, enter dielectric constant e in cell H21 and conductivity, S, in cell H22, guided by Table 5.4 (for sea water s = 81 and S ~ 4). In cell H23 enter, as a positive dB value, the loss of effective RCS or one-way echo strength caused by target tilt or polarisation.

14.2.9 Results and user panels The results panel (km/nmi units of cell F4, repeated in cell J5) shows: probabilities of detection at the spreadsheet range next below two user-selected ranges, the minimum and maximum ranges giving the required PD? the range bracket and fill through which

that PD is achieved, horizon range, ranges of the first two (longest range) multipath peaks and nulls, maximum sidelobe range and the sea clutter horizon range for /? = 0. Cell J21 gives the reference free-space echo strength (figure of merit, Fi 2) at 1 km for a 0 dB m2 RCS target (always km; not scaled according to cell F4; reduced to suit the Gain setting, cell F20; but not swept gain, cell F21), calculated using Eq. (4.12), including physical losses such as Lx and feeder losses affecting echoes and clutter returns, but excluding processing loss L p . Multipath and atmospheric loss terms are excluded. Horizon and J21 are always calculated, even if the horizon and 1 km are outside the spreadsheet range or maximum instantaneous range (MIR). Horizon uses free-space range equation Eq. (5.22b) (including k). Most of the result cells J7: J21 are derived from the main calculation matrix, see Sections 14.6.7 and 14.7. Logical IF functions show >F6 or MIR if beyond the maximum instrumented range, the maximum range in cells B26:B31. Cell J13, per-unit fill, calculates, unless insufficient data is available, the proportion of the range interval between minimum and maximum detection ranges at which detection occurs. Cell J20 gives the maximum range to which sidelobes are detected. Cells AU29, AW29, AY29, BA29 and BC29 perform preliminary range calculations. The User Panel, cells K3 : EX21 to the right of pi, facilitates charting results to bases independent of range. For example, to chart how performance varies with scanner height, //, proceed as follows. First enter in cell 14 the name of the independent variable, here H. Enter the lowest value of interest, say 1 (m) in cell J4. In the cell in which the independent variable is usually entered, here D12, enter = J4, so the spreadsheet adopts the value entered in J4. Cell J5 reminds of the scaling km/nmi and cells J7: J21 compute results of the dependent variables as usual. Use the Copy and Paste Special, Insert Value procedure to place J4: J21 values into cells K4: K21. Reset J4 to a new value of the independent variable, say 2 (m). Again Copy and Paste Special, Insert Value the new contents of J4: J21 into the next column, L4:L21. Repeat as often as desired. A chart may then be constructed to a base of the chosen independent variable, here H row K4 onwards as abscissa, with up to six quantities chosen from rows KIl :K21 as ordinates. Pasted quantities in column K onwards are simply numbers and do not respond to subsequent page 1 parameter changes. Chapter 15, Section 15.2.3, Figures 15.17, 15.21 and 15.22 below is an example. It is prudent to double-click function key f9 after entry of new values to ensure the spreadsheet recalculates properly. Readers of Chapter 13 will need no reminding that display of a result to numerous significant figures does not infer great accuracy. Most of the trailing digits have no practical significance, but are retained to show trends.

14.3

Geometry panel

14.3.1 Layout The body of the spreadsheet calculates each parameter leading to detection as a row, with each of a set of ranges as a column. Column A names the parameter, B the main text equation(s) on which it is based, C its symbol and unit. Column D sometimes

contains miscellaneous items. Columns E to EX are devoted to a set of 150 range values, rising approximately logarithmically from km equivalents of cell F8 value to cell F6 value. It is not normally necessary for users to inspect the Geometry panel, except to scrutinise trends when an unexpected result is delivered. Values are not rounded, so trends are apparent even when a cell scarcely differs from its neighbour. The spreadsheet refers to a number of internal parameters which are not rangedependent and are named and calculated in Table S3 cells M29: BU30, or the other tables. The column E cell of a row is occasionally calculated differently from the remainder and is then identified in the spreadsheet by bold type. In the following, # represents the letter(s) of the column under discussion. Factors of 1000 and 7r/180 frequently appear, reflecting the mixed m/km and radians/degrees units in page 1. Row 32 is not used.

14.3.2 Establishment of a and R series To establish a rising, nominally logarithmic, series of range values (numerically in geometric progression), the working set of columns are first numbered, cells E34: EX34 being labelled serially from 1 to 150. The next row contains the tentative geometric range series, described in Section 14.2.5. This indirect approach avoids the difficult direct calculation of grazing angle from the system geometry. The grazing angle, a rad, for range E35 is calculated in cell D36 per Eq. (5.14d), which is accurate only at short range. The remaining cells are calculated similarly: #36 = D36 x BC29 x E35 x (BC29 - E35)/(l/#35 - 1/BC29). For convenience the terms in bold are pre-calculated in cell D35. This empirical formula yields a set of falling a; incremented per cell BK29, going through zero at the horizon, with shallower slope at longer range, from a maximum consistent with the adopted minimum range to a value algebraically suiting the adopted maximum range. Beyond the horizon, row 36 range increments are exactly logarithmic so ranges rise in geometric progression; meaningless negative a values are displayed but not used. Row 37 calculates grazing point range, Dl km, from Eq. (5.12a); again meaningless post-horizon values are not used. Row 38 calculates the final set of target ranges, R km, from Eqs (5.10) and (5.12b) out to the horizon, and in geometric progression beyond. These ranges may differ slightly from row 35, but their progression remains substantially geometric throughout. They are accurate for the a values of row 36 and form the main charting abscissa. Cell E38 and EX38 values are scaled for entry as minimum and maximum achieved ranges in cells F8 and F6, respectively. The following two rows compute log R and R/RUOR- Row 52 gives \og(R/RuoR), range in nautical miles is in row 73 and log R^ is in row 82. They are available as bases for charts having range-related abscissa.

14.3.3 Scanner and target heights Rows 41 and 42 compute effective scanner and target heights Hr, h\ respectively, from Eq. (5.9a), falling from near the cell DIl and FIl actual values to zero at the horizon. Meaningless negative post-horizon values are not used. Row 43 computes the indirect/direct ray path length difference, A m, from Eq. (5.16a). Again this gives meaningless and unused post-horizon results (here positive).

14.3.4 Angles and effective scanner gain Rows 44-48 compute the geometrical angles summarised in Table 5.1, using the equations there listed. The grazing angle at the target foot, fi rad, row 48, is made to shows zero instead of negative values when the foot is below its horizon, so giving zero sea clutter. The direct and indirect rays to the target, and the sea-clutter ray to the target foot, are in general below the scanner beam axis (unless the axis is depressed) so the effective scanner gain is reduced below cell D8 value by an extent dependent on: (a) the elevation beamwidth, cell D7; (b) scanner depression angle, 8 degrees D13; (c) angles K and x (Figure 5.8(6)); (d) the elevation pattern, cell D12. The gain reductions, T71S, —TK-$9 Tx-$ dB, for the range in question are computed in rows 49-51, respectively, by reference to Table S2.

14.4

Environmental effects

14.4.1 Diffraction region Row 53 computes —<J> (Eq. 5.16b) (to get a set of rising values to suit HLOOKUP syntax), row 54 repeats target range, row 38, for internal HLOOKUP purposes and 55 contains the negative of diffraction region multipath factor m^, computed by Eq. (6.7b), using values for L, U9 Z, z, f(Z) and f{z) per Eqs (6.8)-(6.11) in Table S3 cells N30: Y30. Row 56 gives a monotonically rising set of values from the inverted bell-shaped row 55, returning the artificial value —999 when the slope of row 55 is falling. Cell D55 gives an artificial value which assists calculation of cell E56. Cell D56 gives the minimum of -Wd, used in cell AC30 to bias the working diffraction multipath threshold down from —20 dB when working with low H and h.

14.4.2 Interference region multipath Row 57 repeats column number for Lookup purposes. Divergence, d, is computed in row 58 using Eq. (5.22); d is not used beyond the horizon and an IF function sets to zero to prevent disconcerting show of ERR (error). Rows 59-65 compute the parameters C to K used in sea forward reflection calculations, Eqs (5.40), and po itself is computed in row 66 from Eq. (5.4Of), followed by the associated phase angle, \//, row 67, from Eq. (5.4Og). In row 68 comes the total interference region indirect ray phase shift 0 rad (Eq. (5.16c)), given as — = —(O -j- x/r) to get a rising series of values. Row 69 computes roughness term Y used when finding coefficient of surface roughness, p s , per Eq. (5.41a), followed by ps itself in row 70, using Eqs (5.41c) and (5.4Ie). Differential gain loss, gdif , numerical between direct and indirect rays r * - s , -Tr1S, rows 50 and 49 is computed in row 71 and under most circumstances is close to 1.00. Forward reflection coefficient, p numerical, is then computed in row 72 using Eq. (5.39). Row 73 gives range in nmi; it is inserted here for convenience of HLOOKUP functions in Table S2. Row 74 gives O for charting use. Row 76 shows

the multipath region for the range in question. These preliminaries clear the way to computation in row 77 of interference region multipath factor, rap dB, using Eq (6.4). For row 75 see Section 14.5.1.

14.4.3 Transition region multipath The transition multipath factor, mt, is found by the curve-fitting method of Chapter 6, Section 6.6.2. The lower boundary of the transition region, RA km, is set by cell AE30, the criterion being the path length phase shift in cell AA30, set to 4> = Tt/2 rad. The upper boundary, R^ km, is set by cell AI30, the criterion being m^ = —20 dB, cell AC30 unless a lower value (—cell D56) is needed for low H and h. Cells AG30, AK30 looks up the column numbers for RA, R^. Ranges RA, R^ (cells AM30, AO30) are found by stepping forward 1 column from R'A, R^ and using Lookup functions against the column number, row 57. Multipath values at these ranges are obtained by Lookup and shown in AP30: AW30, with slopes SA and SB in cells BD30: BG30. For convenience, various functions of the general form R^ — RA (Section 6.6.2, factors c, d and e) are computed in cells AX30: BC30 to facilitate computation of factors s, r, q, p in cells BH30: BO30 per Eqs (6.22), (6.18), (6.21) and (6.20), respectively. Row 78 uses these factors to compute mt per Eq. (6.15). If the whole spreadsheet lies in the interference region, some of the Table S3 cells show ERR. This is not significant.

14.4.4 Overall multipath factor Row 80 chooses, by IF function, the overall multipath factor, M, from the interference (row 77), transition (row 78) and diffraction (row 79, = —row 55) multipath factors according to row 76 value. If the whole spreadsheet lies in the interference region, transition and diffraction region multipath factors show ERR and row 80 equals row 77. In this spreadsheet, M applies both to interrogate and return legs.

14.4.5 Atmospheric loss The range bracket through which precipitation occurs is the row 38 range, multiplied by H13 unless per-unit precipitation extent is set F6 or 0.25 m. Horizon range (cell J14) is computed to target tip. The target height used to compute target range, R, in row 38 is AC29 x AK29. 4. Cell E13 shows RCS, dB m 2 /m 2 if coast was entered in cell FlO; enter RCS, dB m2 per square metre of coastline in cell F13, typically —14. If FlO was entered other than coast, cell E13 shows Total RCS, dB m 2 . Enter the target total RCS, dB m 2 , in cell F13. Cell F14 shows the RCSm 2 /m 2 (i.e. the numerical reflectivity) or total RCS m 2 , respectively. 5. If F10 = coast, cell E15 shows N/A and cell F15 need not be entered. Otherwise, E15 shows Extent, radial, m; enter the radial extent of the target echoing surfaces, (the transverse width seen by the radar, metres). In cell F16 enter the axial extent of the echoing surfaces (this applies to both coast and ship). Width of a ship head-on to the radar would be entered in F15 and length in F16, interchanged for a beam-on ship. 6. Enter the target Swerling Case in cell F17 as for a point target (0, 1 or 3; most extended targets are Case 1, the default setting). In the Results panel, instead of multipath peak and null ranges, which do not apply to extended targets, cell Jl 5 shows azimuth overspill range for ship targets or N/A for coast, obtained from the geometry via cell BQ29, the overspill range, km. Cell J16 shows rough-sea critical range, Rc, from Eq. (9.14b). Cells 117: J19 are not used.

14.9.2 Remainder of spreadsheet Row 42 shows target effective height, h\ falling below nj as range increases. Row 74 computes r' jhl (Eq. (9.1Id)) preliminary to computation of mp in row 77 using Eq. (9.12a). Rows 78-80 compute rat, ma, and M as before. Meanwhile row 82 computes the sea-state dependent version of the critical range, R'c km, by Eq. (9.14c). This is not used in the spreadsheet, but is available for plotting.

A B 1 n, Extended passive target spreadsheet „I Date 4 Transceiver 5

C

D

User I Scanner and feeder Type

Type

YACHTRADAR Frequency, MHz 9450 0.0317 Wavelength, m 8 TxP,kW 9 TxP,dBW 30.00 10 Tx loss Lt, dB 1 11 Rx loss Lr, dB 0 12 Service loss Ls, dB 2 13 RxNFN,dB 3 14 RSGthld,dBm 2 -10 Reqd PD 0.6 With screening 0.600 17 Reqd Pfa expt, F -6 18 Proc loss, Lp dB 8 *" Integ, n, c, cr, p = non n 20 Scan/scan corrln y/n y 21 22 23 24 25 TABLE Sl, Mode Max R 26 1 3 27 2 6 30 7* 3 29 4 30 5 * 6

Figure 14.2

0

Az beamwidth El beamwidth0 Gain, dB Efficiency, p.u. Loss, dB Height H, m El part, 1 = sin, 2 = invc Depression0 Rotation, rpm CP improvement, dB Sidelobe below D8, d Tolerable SL PD Feeder ohmic loss, d VSWR Reflcoeff Mismatch loss, dB EIRP, dBW System NF, dB Max R, km 5.555555556 11.11111111 55.55555556 0 0 0

E

F

Spreadsheet Ref |sS2vl Task I Chapter 15, Range bracket Scaling, km/nmi nmi Max reqd R 25 4 Achieved 25.000 20 Min reqd R 0.5 24.5 Achieved 0.367 0.90 Target type 1 Kind: ship, coast coast 4 Tip height j, m 15 1 Height factor, n 0.66 0 RCS, dBm2/m2 -15 30 RCS, num 0.06 N/A 5 27 Extent, axial, m 1 0.1 0 Swerling Case 0,1,3 0 2 Operatoi 0.333 Pol, h, v, c h 1.53 Gain control, dB 0 51.97 Sw Gain control, 0 6.29 SP = s,LP = l s

Plslgth, SP 0.05 0.25 0.5

G

H

Sec 15.3.1.

I

J

|

I

Environment

Results

Type Refraction, k EffEarthradE,km Precip type: Stratiform = Fog vis, km Equiv rain for atten RCS, dBm2/m3 Loss Ip, dB/km Extent, p u Air temp, C RH,% CIr air loss, dB/km Wave hgt, hs, m Sea state WindfctrC2,dB Screening, p.u. Surface dielec, eta conductivity, S Tilt/pol loss l:way dB

Mode, Table Sl 1 PRF, pps LP, y& Rx bw, MHz 25 5 3

5000 5000 2000

2 12742.00 7 0.05 2.266 -9999.00 0.024 1 4 100 0.009 0.025

Scaling Test Rl PD at Rl TestR2 PDatR2 Min R for Bl 5 PD Max R R bracket Fill, p u Horizon R N/A R crit

-2.5 0 Max sidelobe R \ 81 Ref echo, 1 km, FS 0.24 Sea clutter horizon \ 0 Active mod 1 2 3 4 5 6

Selected, pis 0.05 0.25 0.5 O O O

nmi 4 0.6029 5 0.0304

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